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REPORT 


OF THE 


THIRTIETH MEETING 


Vie 
' Rieti foN 


OF THE 


BRITISH ASSOCIATION 


FOR THE 


ADVANCEMENT OF SCIENCE; 


HELD AT OXFORD IN JUNE AND JULY 1860. 


LONDON 
JOHN MURRAY, ALBEMARLE STREET. 
1861. 


PRINTED BY 


TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET. 


CONTENTS. 


Onwmeers and Rules of the Association”. 25.2... .ceccscacc ccs ccouee'ees as 
Places of Meeting and Officers from commencement ..........+00+00 
Treasurer's Account 

Table of Council from commencement ...........0.eescesescocccecccene ves 


Page 
XVii 
XX 
Xxiv 
XXV 


eee ema LACT CIN! bate ek cecetccidea¥odiae cbals coc caanegucednere +’ eccewececsaes KEVIIL 


Officers of Sectional Committees 

Corresponding Members.. siahdioale Su Uvabaiiationick 

Report of the Council to the Gentstal Cendaitibe Senay asacWet clasp aet sat 
Report of the Kew Committee weahes 

Report of the Parliamentary Committee .......ssceeceeceeeeseeeseecee ees 
Recommendations for Additional Reports and Researches in Science 


XX1x 
Xxx 
XXX 

Xxxi 
xliv 

xlv 


PrmmmmPT ONG. GATES 5. uc cau ads cacao ceacaressaceessovevas ves ecchvsses XIVIIL 


General Statement of Sums paid for Scientific Purcases Reena teen 
Extracts from Resolutions of the General Committee 

Arrangement of the General Meetings Raneke(canane ney atte 
REESE FODUICW nu pass onicins-nnacis axeikns acandhebn sos seeson den aus seh soe 


REPORTS OF RESEARCHES IN SCIENCE. 


Report on Observations of Luminous Meteors, 1859-60. By a Com- 
mittee, consisting of James GLAIsHER, Esq., F.R.S., F.R.A.S., 
Secretary to the British Meteorological Society, &c.; J. H. Giap- 
STONE, Esq., Ph.D., F.R.S. &c.;. R. P. Ga a: BGS... &e. ; 
and I. J. Lowe, Esq., F.R.A.S., M.B.MLS. &c. 

Report of the Committee appointed to dredge Dublin aay ‘By ue R. 
Kinauan, M.D., F.L.S., Professor of Zoology, Government School 
of Science applied to Mining Aue the Arts: si..5s05s 

Report on the Excavations in Dura Den. oy fis: Rey eas 
PMRMBISTS (NaMNE) oP ss re eig ee ccs creclelh asic nciriee\dee's odoatcdaeee secs ssdeccterces 

Report on the Experimental Plots in the Botanical Garden of the Royal 
Agricultural College, Cirencester. By James Buckxmay, F.LS., 
F.S.A., F.G.S. &c., Professor of el and whe 4 mechs Agri 
cultural Coles e: ep casgetoes cos vee 


27 


34 


vi CONTENTS. 


Page 
Report of the Committee requested “to report to the Meeting at 
Oxford as to the Scientific Objects to be sought for by continuing 
the Balloon Ascents formerly undertaken to great Altitudes.” By 
the Rev. Roserr Wacker, M.A.,, F.R.S., Reader in ee 
Philosophy in the University of Oxford. Ae PPer oacesce ys 


Report of Committee appointed to prepare a " Self-Recording Meee 
spheric Electrometer tor Kew, and Portable Apparatus for observing 
Atmospheric Electricity. By Professor W. Tomson, F.R.S. ...... 44 


Experiments to determine the Effect of Vibratory Action and long- 
continued Changes of Load upon ae iron Girders. ee Wit- 


LIAM FairBalrn, Esq., LLD., F.R.S.. a ddgetsnscavees ee 
A eT of Meteorites and Fireballs, coe A.D. 2 to A.D. 1860. 
By R. P. Gree, Esq., F.G.S8 cw sale «=, 48 


Report on the Theory of ates Spare I “By y. 1 Boe 
Smitu, M.A., F.R.S., Savilian Professor of Geometry in the Uni- 
versity of Oxford aiudssisseisensocieeeceesewess soe yas qeuseesanstn=: Meester 120 


On the Performance of Steam- Vessels, the Functions of the Screw, and 
the Relations of its Diameter and Pitch to the Form of the Vesssel. 
By Vice-Admiral MGORSOM 1060. c0ssecsoscasacersdvexoes sefaatbeaeeame eu teaae 


Report on the Effects of long-continued Heat, illustrative of Geological 
Phenomena. By the Rev. W. Vernon Harcourt, F.R.S., F.G.S. 175 


Second Report of the Committee on Steam-ship Performance............ 193 
Interim Report on the Gauging of Water by Triangular Notches 
List of the British Marine Invertebrate Fauna ...,.....sscccccsseeeceneenees 


CONTENTS. vil 


NOTICES AND ABSTRACTS 


OF 


MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS. 


MATHEMATICS AND PHYSICS. 


MaTHEMATICS. 
Page 


Address by the Rev. Professor Price, President of the Section s.secseesseeres  L 
Dr. BRENNECKE on some Solutions of the Problem of Tactions of Apollonius 


of Perga by means of modern Geometry ...scereseseceerereeerersennens aves waaceses 
Rev. James Booru on a New General Method for establishing the Theory of 

CWONIC SECHONS....050..0sccsecescceseccesceserevcncsos aoenoscec0c1-bechnAneesan Sacneaces we 
——____-—____—— on the Relations between Hyperconic Sections and Elliptic 

Integrals...,..... A eee saat oa tede aa acene tactic reddeveverneet soles stasiionrastsneteraceccses wn 
Mr. A. Cayxey on Curves of the Fourth Order having Three Double Points... 4 
Mr. Parricx Copy on the Trisection of an Angle .....sscseseeseseenereeeeerecneusens 4 
Rev. T. P. Kirkman on the Roots of Substitutions .....+...ssesereeee Soenenensne ap 4 
Rey. T. Rennrson on a new Proof of Pascal’s Theorem ....s.seseesseseserreenes aa 8 


Professor H. J. SrepHEeN Smit on Systems of Indeterminate Linear Equations 6 


Professor SyLvEsTER on a Generalization of Poncelet’s Theorems for the Linear 
Representation of Quadratic Radicals ....sseeeese0 sseesevsenes Gaeressspcevasecege> Paes 


Lieut, Heat. 
Sir Davip Brewster on the Influence of very small Apertures on Telescopic 
IWIBIOH cess ccencccscccacascnesssncassevacceccssecascccseses atvacsdepeesreedddnacsresnes hoes 2 if 


——-—-—— on some Optical Illusions connected with the Inversion 
of Perspective......+. ad sieacamanadanslisesrewedesa sf Goan detsmaeeaisesaicaine aaiwarpsawene sa desis 7 


on Microscopic Vision, and a New Form of Microscope 8 
———_——— on the decomposed Glass found at Nineveh and other 


PIACES ......500c0esescnesessarssceseesscosees Se dndins ns coisidel ta cshesowandqanesttanease<¥ayieqse¢ 9 
Dr. J. H. Guapsrone on his own Perception of Colours ......ssseseee caosvgeecceee 12 
—________—_—- on the Chromatic Properties of the Electric Light of 

Mercury ..e.csccsscseeeecesccscesccarecnscnccesetesencuscnssansesenenssasensceeesseuesegses hepeete 
Professor JeLLerr on a New Instrument for determining the Plane of Polariza- 

TLOT wovecccceeecrereeeess eeeeenee wevenecconecsorne ssnaupigedace cette tis sleepin Gealsnniecnelelo's oS 


Professor L. L. Linpesiér on the Caustics produced by Reflexion .s.ssseseseeeee 14 


Professor Maxwe tt on the Results of Bernoulli’s Theory of Gases as applied 
to their Internal Friction, their Diffusion, and their Conductivity for Heat... 15 

_ ——__________ on an Instrument for Exhibiting any Mixture of the Co- 
) lours of the Spectrum......+. bsp eenes SCOREUED CrarSehao canoes seaeinaesasese eaauclensane 14 


viii CONTENTS. 


Mr. Munao Ponron’s Further Researches regarding the Laws of Chromatic 
Dispersion .....ccccccssscscccscccscccscccotssccsscsascesrcrsaccccsss ssn decneestis ie: ne 
Professor Witt1am B, Rocers’s Experiments and Conclusions on Binocular 
WiISIONS. cevsrensseccte(erscsensaanecciureccees eonvseeroest ss -ssesaesesasessesaameemeecnen sce 
M. Serrin, Régulateur Automatique de Lumiére Electrique ...+++seesesseseeeere 
Mr. Batrour Stewart on some Recent Extensions of Prevost’s Theory of Ex- 
CHANG CS 2200 5dc46 casctagdcadvs dace act clvatsds vat lesedec1seds ckdebecatescdseatadeenesstel wiees 
Mr. G. Jounstone Stoney on Rings seen in viewing a Light through Fibrous 
Specimens of Calc-spar......-sseseeeeee Sused decbouscuesiecssseaseuenteusettamadatclcsmiacs 


Mr. R. Tuomas on Thin Films of Decomposed Glass found near Oxford ....... 


ELecrricity, MAGNETISM. 


Mr. Joun Atxan Brown on certain Results of Observations in the Observa- 


tory of His Highness the Rajah of Travancore ....sscsseseeceseeeeeees = debdoae ate 
— on the Diurnal Variations of the Magnetic Declina- 

tion at the Magnetic Equator, and the Decennial Period .........:ccsssseeeeeeeees 
Sas — on a New Induction Dip-Circle ......0...ccsasessesnsanc 


— ——_—_____.__. 


on Magnetic Rocks in South India........s.esseeeseeee 
on a Magnetic Survey of the West Coast of India... 


— on the Velocity of Earthquake Shocks in the Late- 
PRE OF DG cies cost as age? va 8i vadsacusates ik cedaths sad satsestesanahtnugaxcdeiees tiers ‘ 


Mr. A. Crarke on a Mode of correcting the Errors of the Compass in Iron 
Ships ..... Sasowoerese cesses scdusoscausaviaspessrssdavessceeeccseacacite setovedesispameeeenennnd 


Sir W. Svow Harris on Electrical Force ....ssssssesscccseeceeee javeatacensaeeeaesses 
Rev. T. RANKIN on the different Motions of Electric Fluid ...s.....ceseees Soa otvek 


Professor W. B. Rocers on the Phenomena of Electrical Vacuum Tubes, ina 
letter to Mr. Gassiot ...... seeGaecevaesSis rach s cueteseelasecehe ee eec eee eee epee Sastaces 


M. H. von ScutaGintwerr’s General Abstract of the Results of Messrs. de 
Schlagintweit’s Magnetic Survey of India, with three Charts .....ssscesseeees & 


M. Werner and Mr. C, W. Siemens, Outline of the Principles and Prac- 
tice involved in dealing with the Electrical Conditions of Submarine Electric 
Telégraphs POOP cee tere tneeesesdbeseos oer 


——S 


—_— 


POCO Pere ee meee Eee ee RE R OHHH EEE E HEH OEE DEES SEES 


ASTRONOMY. 


Mr. W. R. Birt on the Forms of certain Lunar Craters indicative of the Ope- 
ration of a peculiar degrading Force ...s0..0... itegevesecancacee osceetebelawenececss 


Professor Hennessy on the Possibility of Studying the Earth’s Internal Struc- 
ture from Phenomena observed at its Surface 


Rev. Epwarp Hrincxs on some Recorded Observations of the Planet Venus in 
the Seventh Century before Christ 


Mr. R. Hopeson on the brilliant Eruption on the Sun’s Surface, 1st Septem- 
berstS5Ou.n smear eee ccercenccencctsersceseene 


Dr. Jonn Lex’s Prospectus of the Hartwell Variable Star Atlas, with six Speci- 
men Proofs.........4; : 


POPPE ee reer ee ee Peeresens Cee eeereeesnees Peete eeetee 


Professor B. Pierce on the Physical Constitution of Comets...ssssesssssseeseeees 
een niencmeenes On the Dynamic Condition of Saturn’s BIBUB ascbeoseenene 


Page 
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30 


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32 


CONTENTS. 


Professor B. Pierce on the Motion of a Pendulum in a Vertical Plane when 
the point of suspension moves uniformly on a circumference in the same 


LIFE aadcdcaicoruucecarcotrdscctadcveccsilccecscdsssaetenvecMMes topernerssdsectandaseqssens 


MerrEOROLOGY. 
Mr. Jouw Baz on a Plan for Systematic Observations of Temperature in 
Mountain Countries.........sseseereeeee Sdoetidococta semenneanenisesnd wiatecesaeces pease 
Mr. W. R. Bret on Atmospheric Waves ....++.+se++++ -eridnnncce Kepsseenesis Stee casnt 
M. Du Bovutay’s Observations on the Meteorological Phenomena of the Vernal 
Equinoctial Week ..........++4++ Raeaece see nadi te sesh ane sPaneen Rae semaseehiee.s sachs “ce 
Mr. R. DowpeEn on the Effect of a Rapid Current of Air ....+.eeesseeeess yanekaesis 


Admiral FrrzRoy on British Storms, illustrated with Diagrams and Charts... 


Mr. J. Park Harrrson on the Similarity of the Lunar Curves of Minimum 


Temperature at Greenwich and Utrecht in the Year 1859. ticussscessansperarcsst 
Professor Hennessy on the Principles of Meteorology ......... = pesoonncentearodee : 
Captain Maury on Antarctic Expeditions .c.......--.++++ Rancentenpcsscasacsms ss acoso 


on the Climates of the Antarctic Regions, as indicated by Ob- 
servations upon the Height of the Barometer and Direction of the Winds at 


Sea........ Be cates TEC Cn SLE PCR CORO EEET Cor ceeeeee Scere Lcocedent pecs seneanendees er 
Rev. Henry Mosetey on the Cause of the Descent of Glaciers .....+--++++..+0+ : 


Rev. T. Ranxtn on Meteorological Observations for 1859, made at Hugagate, 
Yorkshire, East Riding ...... Ht SPREE tronat ss ceeset tas sieberetene ere 


M. R. pe Scuracintweir on Thermo-barometers, compared with Barometers 
at great Heights ............+ beattcnaecetarcctebe dese Reaack vets shee parte eeVab cues seek is 


Captain W. Parker Snow on Practical Experience of the Law of Storms in 
each Quarter of the Globe... ..csecsseeeceeceeeeseees eeseresasas att qaeeaease Onsen ens eee 


Mr. G. J. Symons’s Results of an Investigation into the Phenomena of English 
Thunder-storms during the years 1857—59.........- puacavene Sev saetseneescae 


ee eeeeee 


Professor Witt1am THomson’s Notes on Atmospheric Electricity ....... Banduthie 


M. Verpet’s Note on the Dispersion of the Planes of Polarization of the 
Coloured Rays produced by the Action of Magnetism* ....... pcb daWaouehaavege vee 


Mr. E. Vivian’s Results of Self-registering Hygrometers...secsssseseereserereees re 
Rev. A. WELD’s Results of Ten Years’ Meteorological Observations at Stony- 


PARSE Peacisccccoscccccccscccctccccccceccccccecesansecccccncesravoccvecttnessverovessvesstoseve 


GENERAL Puysics. 


Mr. J. 8. Sruarr GLenniz, Physics as a Branch of the Science of Motion ... 
a General Law of Rotation applied to the Planets 


el 


SounD. 


Rev. S. Earnsnaw on the Velocity of the Sound of Thunder......seeceseeeseesane 
on the Triplicity of Sound ...-..sceseesecersereeeeeeeeeeeeeneeeens 


INSTRUMENTS. 


Mr. Parrick Aptz’s Description of an Instrument for Measuring Actual 


MIBTATICES ccccccceccecccccdsccecececacccecseascasceccocesccccssccnsrncansocoresccccensncecsres 


* This should haye been placed in an earlier division. 


56 
58 


58 
58 


59 


> he CONTENTS. 


Mr. Parrtck Apte’s Description of a New Reflecting Instrument for Angular 

Measurement pcr deneauacseceaes ss saeeenet <anete Merete eae senasbale a riceien © wep aieeiiaiaee 
M. E. Becqueret on a Pile with Sulphate of Lead.......... cep patie astemogel eater ~ 
The Hon. W. BLanp on an Atmotic Ship.....csce.cecerecccsovesees Sesawne dese eweeee sos 


Rev. J. Boorn on an Improved Instrument for describing Spirals, invented by 
Henry Johnson ....... BO PRRCRO CIEE rerONAGR A Idoshuctnsacne sacbae nn dee se once pareeatemas 
Mr. A. Craupet on the Means of increasing the Angle of Binocular Instru- 
ments, in order to obtain a Stereoscopic Effect in proportion to their Mag- 


TURIN EAP OWED eee wactisavee do cvee ed daemccoeiepe sagen acicdcideemeteicees alas Ssieacseveceuverdeae 
—_— on the Principles of the Solar Camera.........ssscessessssecneseees 

Mr. Henry Draper on a Reflecting Telescope for Celestial Photography, 
erectine at Hastings; near INewiMOrkr.;ccdcsasceasece cevecs teeter esseewtaseveenmece eee 
Mr. W. Lapp on an Improved Form of Air-Pump for Philosophical Experi- 
ments ...... tee ceeerecseneeccsceeeres eee ececeeceereceessereeescceences teeccveceveveccreeves eee 
Mr. Joun Smira on the Chromoscope ..e.esseseeee Ninenecassnansensccascsesegamtaes bss 

CHEMISTRY. 

Professor ANDREWS OD OZONE ....cecsesesssecseneeseenees Sompanen tatoos ee oansyan ned amgle 
Dr. Brrp on the Deodorization Of Sewage)...ccscy<csessessosecececesecrsvusoanssnseneus 
Professor B. C. Broprz on the Quantitative Estimation of the Peroxide of 
Ly rOpent cern ves-ncets ss aceceseessseaes SACLECET DOHCOEBE Ton J0bk ERO aC anorectic ree one 
Mr. G. B. Buckton on some Reactions of Zinc-Ethy] ..........ssesssscseesecsesees 
Mr. J. J. Coteman’s Note on the Destruction of the Bitter Principle of Chy- 
raitta by the Agency of Caustic Alkali.........ccscossscceescesscesecsecreseeereees oes 


on some remarkable Relations existing between the 
Atomic Weights, Atomic Volumes, and Properties of the Chemical Elements 


Dr. FrANKLAND and B. Duppa on a new Organic Compound containing Boron 


Dr, GrapsTone’s Chemical Notes .......2-scccccsssccececore See teviqacodeuseedsepsigareirs 
Mr. W. R. Grove on the Transmission of Electrolysis across Glass ...... beans 
Mr. A. Vernon Harcourt on the Oxidation of Potassium and Sodium........ 
Mr. J. B. Lawes and Dr. J. H. Grtperr on the Composition of the Ash of 

Wheat grown under various CIrCUMStANCES .....ssececreseceeeeeeeeesenneeeeeeeaees . 
Professor W. A. Mixxer on the Atomic Weight of Oxygen.........sssseseeeees ee 
C. Moritz von Bosr’s Remarks on the Volume Theory .........00e0+. coeuteye eee 


Mr. Warren De ta Rue and Dr. Hugo Muxtuer on a New Acetic Ether 
occurring in a Natural Resin......... Sanetps Pam uen tenants easton tcl: cctaes sen ceest items 


on the Isomers of Cumol ......... Gekcaaouswases dvanoccucaeaane 


Dr. Lyon Pravrarr on the Representation of Neutral Salts on the type of a 
Neutral Peroxide HO, instead of a Basic Oxide Hy On ....c.secccveceseesenees rer 


Professor T. H. Rowney on the Analysis of some Connemara Minerals ....... 


on the; CompositioniOf Jebrccc.csts.mensress coves oseewenes 
Mr. T. Scorrern on Waterproof and Unalterable Small-arm Cartridges........ 
Dr. HerMANnn SpRENGEL on a New Form of Blowpipe for Laboratory Use... 


Dr. Tuupicuum on Thiotherine, a Sulphuretted Product of Decomposition of 
FAT DUMINONS SUDSEAHCES nec seinee ds ve cede once -useedal cheated Spence sebastienesa ener 


Professor VoeLcKer on the Occurrence of Poisonous Metals in Cheese ..... rey 
Dr, W. Wattace on the Causes of Fire in Turkey-red Stoves,........+006 Scheo: 


66 
66 


71 


CONTENTS, 


GEOLOGY. 
Baron F. Anca’s Notes on two newly discovered Ossiferous Caves in Sicily ... 
Sir Davip BrewstTer’s Details respecting a Nail found in Kingoodie Quarry, 


A Voriecieianicinicis’sls ce olcoesinnie sis(cin cite slanibisie pale. 00 eves races sc@iis oturecisseceedse ceeds susecaesne 
Rey. P. B. Bronte on the Stratigraphical Position of certain Species of Corals 
ray id fey UTES Reeersoneeee Sesh dane oababndcne ancuddnecesaron ction sartei co Btbdo. dudenadsadadssddoon 
Mr. Joun ALtan Brown on the Velocity of Earthquake Shocks in the Laterite 
RMA eceadvcaengnicceainsleascicecuecsveceossvesceescnasat severest se "Sinn Hiesonudnecescn ona 
Rev. J. C. Crurrersuck on the Course of the Thames from Lechlade to 
Windsor, as ruled by the Geological Formations over which it passes......... 
Professor DAuBENY’s Remarks on the Elevation Theory of Volcanos ......+404+ 
Rev. J. B. P. Dennis on the Mode of Flight of the Pterodactyles of the Copro- 
lite Bed near Cambridge ....--ssssseecseseesereneees nagebaeoonDOOhOr Cote naceROnoSeteS nv 
Rev. J. Dinexz on the Corrugation of Strata in the Vicinity of Mountain 
Ranges ccecseceseseseeeeees Sa nencidepSaneosc nc LUO OEOCDOBRCAODL CEH Ca BEAcne Soneceacviensnaeas 
Sir Parzre pE M. Grey Ecerron’s Remarks on the Ichthyolites of Farnell 
FUGa ie sacesicseceaeaisesesiisics ss pecan seers Bocrenadnee aneagsdacoonaynddagode Sciggadonadanebnne 
— on a New Form of Ichthyolite discovered 

by Mr. Peach...cccesssesseseseeeereeass cannasboncnte deeabanace Sebensecssnrseus saneaoneincore 
M. A. Favre on Circular Chains in the Savoy AIps....ccscsesesscerssecceeeerseeens 
Mr. ALeuonse Gaces on some Transformations of Iron Pyrites in connexion 
with Organic Remains...... scp COEEBE So SELORO IA00080N peehiterantes Ropn ee deeiaxaneeseeens 
Dr. Gernitz on Snow Crystals observed at Dresden ......eseeveeseeeees SCE CDAD 
— on the Silurian Formation in the District of Wilsdruff..........c0000+ 
Professor Harkness on the Metamorphic Rocks of the North of Ireland ...... 
Dr. Hecror’s Notes on the Geology of Captain Palliser’s Expedition in British 
INorth AMETICA ....002:.0ceccseccenscresececesonacnccsvasasoasaccereresses J gapnr pesanagabedn 
Professor F. von Hocusterrer’s Remarks on the Geology of New Zealand, 
illustrated by Geological Maps, Drawings, and Photographs...... Sreidachiasendcor 


——______—_  — Observations upon the Geological Fea- 
tures of the Volcanic Island of St. Paul, in the South Indian Ocean, illus- 
trated by a Model in Relief of the Island, made by Captain Cybulz, of the 


Australian Artillery......esessee eatasratee lelesielve's cbopeaeuaeanigy estes SAR NSDUCEOD Beteenne 
Mr. E. Hutt on the Six-inch Maps of the Geological Survey ......sssseseeseeenee 
on the Blenheim Iron Ore; and the Thickness of the Formations 

below the Great Oolite at Stonesfield, Oxfordshire ........ssesseeceeees SASEPaC AAA 
Mr. T. Sterry Hunv’s Note on some Points in Chemical Geology ...sse++s0+ 
Mr. J. Beets Juxes on the Igneous Rocks interstratified with the Carbonife- 
rous Limestones of the Basin of Limerick.......sceesseerees MPN ce cadianeeadesesss 
Mr. J. A. Kwipz on the Tynedale Coal-field and the Whin-sill of Cumberland 
and Northumberland.......ccssscesesereeeees EERO Ac SdoAeDeCEnCoN Rcdudemniiceswcnares 


Dr. W. Lauper Lrypsay on the Eruption in May 1860, of the Kotltigja Vol- 
CANO in Iceland.......ssccssoscecseecovcssrocecsesscccscscovesssccosccsssasnveccssonacceces 


Rey. W. Lrsrer on some Reptilian Foot-prints from the New Red Sandstone, 

north of Wolverhampton......sscssssccecseesereeecenccneassasecaeeeeueereusseseesenserees 
Rev. W. Mitcue x and Professor TenNant on the Koh-i-Noor previous to 

Hts Cutting....0......sccsscceveeeseetecs * Choon Bonpe a DnISS Ca pbuCenIaochC nat sabe ne bandas 
Mr. C. Moors on the Contents of Three Square Yards of Triassic Drift ........ 
~ Mr. Wirt1am Motynevx’s Remarks on Fossil Fish from the North Stafiord- 
shire Coal Fields ..sscsscsesseseeseaeres paamieoeslenstiess Seantiotogean Benatar san adeseescsiines 


bt 
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xli CONTENTS. 


Page 
Mr. J. Powrtx’s Notice ofa Fossiliferous Deposit near Farnell, in Forfarshire, 
INA Bc scocnaenas ser asdecuecnrcnses daeancsoemetcnteeneanasianes creer ace arr cent neeee re eeenee 89 
Professor Puriurps on the Geology of the Vicinity of Oxford .........sece0eeseeees 90 
Mr. JosEpH Prestwicu on some New Facts in relation to the Section of the 
Cliffvat MundesleysINortolk:s.cccseuesesseasanecrestarewsscccrecsec eee adac eeeeaaeene 90 
Mr. /J.)Prich on Shckensid@ss.c..s-sssuscsessssseceseeten sv eceeds “See reeacno eaeclees Senate 91 
Mr. Witi1am PeNncELLy on the Chronological and Geographical Distribution 
of the Devonian Fossils of Devon and Cornwall ........,.cccssecessccecccccececsece 91 
Professor H. D. Rogers on some Phenomena of Metamorpiisnts in Coal in the 
SHUMILCE SCALES oe, csct ssesdeasdersacensoceccecccrescurstscsessevesenererasasarett eset eeeiaee 101 
Rev. Professor Sepewicx on the Geology of the Neighbourhood of Cambridge 
and the Fossils of the Upper Greensand ............. Sos voce nsceseaseastsentsisaeanperans 101 
Rev. Grisert N. Smiru on three undescribed Bone-Caves near Tenby, Pem- 
rOkeShivGweceacceamnceeates sass cman cresceene case inedensaneste see serer ee Wola dane «teaeeengas 101 
Rev. W. S. Symonps on the Selection of a Peculiar Geological Habitat by 
some OL the raremsbmbishy Elan tSiewncoacccceccoss«os sairecsesectne sie eee tie te neeme 102 
Rev. H. B. Tristram on the Geological System of the Central Sahara of 
ALGOMA ness erseracsncsciaccitsoadstserecscees sactoretmacdserscabecenercenee st cot tae ee mmeare 102 
Mr. J. F. Wuireaves on the Invertebrate Fauna of the Lower Oolites of 
OxfordShinetgascscsecceceradaess a vaceroecs slices cone secase seston teeteneoee coon ante a aieeee 104 
Captain Woopatt on the Intermittent Springs of the Chalk and Oolite of the 
Neizhbourhood! of Searborotgh..c.3s.: 08s <deccss.c0taessadeaveescessns-apepreseweger 108 
Mr. Toomas Wricut on the Avicula contorta Beds and Lower Lias in the 
South of England.......... Gvesctestacs EG SesOuensut vorbiescewanenseat saesaviesaahaw sy Rime -. 108 


BOTANY AND ZOOLOGY, tncLtupinc PHYSIOLOGY. 


GENERAL. 


Mr. Putrre P. Carpenter on the Progress of Natural Science in the United 
States and Canada...........0+« Paver ead oa ness Pov achaasceaesecrucsutes chadacaeaceset cade 109 


Professor DauBeny’s Remarks on the Final Causes of the Sexuality of Plants, 
with particular reference to Mr. Darwin’s Work ‘ On the Origin of Species 


by Natural Selection’ ......... “Hochortncso sho. eae nceceeer eee ease phaxte anne free 109 
Borany. 
Professor DowpEN on a Plant Poisoning a Plant..........sccssssesecerserseees sesess 110 
Dr. C. Dresser on Abnormal Forms of Passiflora c@ruled ..ccccccecseseresevenses 110 
on the Morphological Laws in Plants ..........cscecesceeseeeeenes 110 
Rev. Professor HeNsLow on the supposed Germination of Mummy Wheat..... 110 
Mr. Joun Hoace on the Distinctions of a Plant and an Animal, and ona Fourth 
Kingdom of Natures. ..~-0cescecysnesensrpnvonrivedesnecoapersetaseessaseeprensesseseseas lil 
Mr. M. T. Masters on the Normal and Abnormal Variations from an assumed 
My pevin Plants. .205 sco. sceasewoes co-i- cae ane=nsinexceeuecsoasscnesrerueniosserscarssecaanenas 112 
Dr. G. OerLviz on the Structure of Fern Stems ....scescseeeeees cass casasueee maces sep TD 
ZooLoey. 


Mr. Frank T. Bucktanp on the Acclimatization of Animals, Birds, &c., in 
the United Kingdom ..ccocssscsscsccenccssesscocesessecsesnccsaveusstunsecauddsvsersecaws. LAGS 


CONTENTS, xiii 
Page 
Mr. Curusert CoLtinewoon’s Remarks on the Respiration of the Nudibran- 
Ghiate Mollusca ...cccccccccsccscsens aaeencinccisecsss cans aM Ran coca asc ateE eer sc cwccsen ce 113 
-————__—_————— on the Nudibranchiate Mollusca of the Mersey 
PATI CE tnt ecadececccdrsscepestestsestcadsstcccsececase cdl Pasceebecavustctphedes desssescas 113 


SEE IVS UEINALIC!ZOOIOPY; ovvientnavoncorseveceenueesecasaussovsvasisessWasenens+serssinesouns 114 


Professor Draper on the Intellectual Development of Europe, considered with 
reference to the views of Mr. Darwin and others, that the Progression of 
ieanjems 1s. determined by Iawiscs.ess.ss0sesccsccsnecsesseceessices ys dnstse-cps'e seaee 115 


Rev. H. H. Hicerns on some Specimens of Shells from the Liverpool Museum, 
originally from the Pathological Collection formed by the late Mr. Gaskoin... 116 


Rey. A. R. Hoeawn’s Notice of British Well Shrimps ....... BG Ta De « LI6 
Mr. J. G. Jerrruys on the British Teredines, or Ship-Worms ............0eeeee0s 117 
Mr. Cuartes W. Peacu on the Statistics of the Herring Fishery......... Preaaes 120 
MPa OESPERTCH ONC yOIP PE. esseces Winn ve cwlcrece es ieteassbste cies nctetecdiencseastysstes 120 
Mr. Lovett Reeve on the Aspergillum or Watering-pot Mollusk ...........0..08 120 
Dr. P. L. Sctarer’s Remarks on the Geographical Distribution of recent Ter- 
BEEP IMVCLECDLALAssa.ssissscessincsesciencondaesserecenersscane Seep idaniiivenasseoesatlsceests 121 
Mr. H. T. Starnron on some Peculiar Forms amongst the Micro-Lepidopterous 
MMR P EM na eeas erestis sauce meanest mcenctciasvece cacostsetene da tr cevecccseressesedesvs 122 
Dr. Vertoren on the Effect of Temperature and Periodicity on the Develop- 
ment of certain Lepidoptera............... es cewies ninelnn penetra elsigas Biss Jeocsceeeeers » 123 
Biro. O., Westwoon on Mummy Beetles, .......ccsrspeosaseyseesessnspeceptenessens 123 
——————— on a Lepidopterous Parasite oecurring on the Body of 
BEML AR OTC RMUCLANT GD a scng's%inniomaidaisaae sss 8sdesPesehesniese ses cosy cs sesesecseceeseasere » 124 
Dr, E, Percevat Wricut’s Notes on Tomopteris onisciformis........000.008 weneqe 124 
PuysioLoey. 


Professor Beatz on the Ultimate Arrangement of Nerves in Muscular Tissue... 125 


Professor VY. Carus on the Leptocephalid@......ccccssesscovsceccoeceoteescevcocedeses 125 
——_—————— on the Value of ‘ Development” in Systematic Zoology 
pdm animal MOT pHOlO Ry? vascc..ssonscaesosncdecsoascavesvcghoabebevepeaesac ouaneowensees 125 
Professor Corset on the Deglutition of Alimentary Fluids...........se00eecccsese 216 
Dr. Ropert M‘Donne tt on the Formation of Sugar and Amyloid Substances 
Rates TEAL EL CORON. os Sa ntindisc Saeasina,s nerves els sealeasoeceopep'vs ap ogosovcemss si. « +. 129 


Mr. Artuur E, Duruam’s Experimental Inquiry into the Nature of Sleep..... 129 
Dr. Micuarx Fosrer’s Contributions to the Theory of Cardiac Inhibition...... 129 


Mr. Rosert Garner on certain Alterations in the Medulla Oblongata in cases 
BMT sa) Voto micns Mesa eeeiseiciee eeck ace oleae eke ee ee eee ek ieeee odds en ckscks 129 


- on the Structure of the Lepadid@.........csceeecesees aonnesere 130 
Mr. Georce D. Gres on Saccharine Fermentation within the Female Breast.. 131 
Sir Caarres Gray on Asiatic Cholera......ses...8 Ruenontesess atiowncdenet oa urcekesanes 132 


Mr. J. Reay Greene, A Word on Embryology, with reference to the mutual 
relations of the Sub-kingdoms of Animals............. seaeneaeenecemesaaecy cesponeses LSD 


Mr. Epwarp R. Harvey on the Mode of Death by Aconite.......sssscssecceeasee 133 


Professor Van pER Horven on the Anatomy of Stenops Potto, Perodicticus 
Geoffroyt of Bennett....... dtleiese vesiseeinneiuniaesey ec teveeevesscscsesscscrscecssecsssosensens 134 


X1V CONTENTS. 


Professor Van prr Horven, Observations on the Teredo navalis, and the 

Mischief caused by it in Holland.............065 SadeoLnonGagsncckecadodanasutidddé foc wee 
Professor Huxtry on the Development of Pyrosoma .......s0eeeenee nencsuee =qpe0bon 
Dr. Cuartes Kipp on the Nature of Death from the Administration of 

Anesthetics, especially Chloroform and Ether, as observed in Hospitals...... 
ib. Lewis ona. Hydro-spirometer ..ccsor0.«arwagecduccsiesecenstundecsstcccmaeae etenciai 
Mr. Joun Luspock on the Development of Buccinum .....scsscsssssscesenseeteenees 
Mr. Arcuigatp MacLaren on the Influence of Systematized Exercise on the 

Expansion tof theiChestsaienecskneeeaensacasmere sree sain Sappeoecriceba secede sna ce 
M. Otter on the Artificial Production of Bone and Osseous Grafts .......0.+ 
Dr. C. B. Rapexirr’s Experiments on Muscular Action from an Electrical point 

OL VIEW. 5 coisas scans sae unc chun sok saeeceuaneneeavarcurcanes eatne naa seue set aman sebews 
Dr. B. W. Ricuarpson on the Process of Oxygenation in Animal Bodies ..... 
Dr. Epwarp Smiru, The Action of Tea and Alcohols contrasted ......seeesseeess 


Page 


136 
136 


136 
139 
139 
142 


143 


143 
143 
145 


Dr. J. L. W. Taupicuum on the Physiological relations of the Colouring — 


Matteriof thesBilessepsscsscuresacess wawseenae MOEA Ncuasnecen ieee juseenaenedees eAddoae : 


GEOGRAPHY AND ETHNOLOGY. 


Opening Address by the President, Sir Roprrick Impry Murcuison .......+ 


Mr. T. W. Atkinson on the Caravan Routes from the Russian Frontier to 
Khiva, Bokhara, Kokhan, and Garkand, with suggestions for opening up a 
Trade Jbetween Central: Asia. and sndia .caucesmaee «cestode sa cteceeapeeereeeeeneee ee 


_——_— on the Caravan Route from Yarkand to Mai-matchin, 
with a Short Account of this Town, through which the Trade is carried on 
between Russiasand) China ccnesctnensscassevtenoeden cmctioncsesenel teas coca 5 


Capt. Sir E. Betcuer on the Manufacture of Stone Hatchets and other Imple- 
ments by the Esquimaux, illustrated by Native Tools, Arrow-heads, &c....++. 


Mr. Joun Crawrurp on the Aryan or Indo-Germanic Theory of Races ....... 


—__—_—___———— on the Influence cf Domestic Animals on the Progress of 
Civilization) (BILAS) sca, casssakpeemeccetenecteone te osmeekar eee. sunetscalesseaateeeemtoeeinc 


Mr. R. Cut on certain remarkable Deviations in the Stature of Europeans.... 


on the Existence of a true Plural of a Personal Pronoun in a 
living European Language scrsnnseccciedsestsdecscssevevseencetseeme Rec doseenasantiesh's 


Captain Cypuuz on a Set of Relief Models of the Alps, &C.....ccscceeceeceseeeees 


Rev. Professor Graves on the Arrangement of the Forts and Dwelling-places 
Gf the Ancient Ubishie: ccs sci dsnactanenset-seearecnaervades tale Arcs eee eaeen aes 


Rev. Epw. Hrncxs on certain Ethnological Boulders and their probable Origin 
Professor I’. von Hocusretrrer’s New Map of the Interior of the Northern 


Island of New Zealand, constructed during an Inland Journey in 1859 ....... 
Dr. J. Hunt on the Antiquity of the Human Race.....e...secseccee sees Scinteray Oroeee 


Mr. V. Hurrapo on the Geographical Distribution and Trade in the Cinchona 
Rev. Professor Jarrett on Alphabets, and especially the English; and on a 
New Method of Marking the Sound of English Words, without change of 
Orthography cmespanceene seen ce veemsee mere cnt Sor sSStarnaonapsas Desir asonscdesodc sob anes 
Mr. R. Knox on the Origin of the Arts, and the Influence of Race in their 
DevelopmMentire Aescntecceceateowenes. cnesisce teeencae seme satteset Crit nenenneSnee eee nae 


Mr. D. A. Laner’s brief Account of the Progress of the Works of the Isthmus 
of Suez Canal...... dic bosKobOHOmadaBroncons chcccosuserbonoddac seve 


Fee neeee ee ereesetesaetee 


147 


148 


153 


154 


154 
154 


155 
155 


163 
163 


163 


CONTENTS, XV 


Page 

Dr. R. G. Latuam on the Jaczwings, a Population of the Thirteenth Century, 
on the Frontiers of Prussia and Lithuania ........scecsscsesssscscneneeeneees ae ace 163 
Dr. D. Livinestone on the latest Discoveries in South-Central Africa.......... 164 

Mr. W. Locxuart on the Mountain Districts of China, and their Aboriginal 
Inhabitants...... Sie oc dccucecOrngdbor CEeSESd br COC NEDIGSORD< SECO RORnDar Jobe Uap ¢RUBOBROBCE DE. 168 
Mr. D. May’s Journey in Bae am and Nupé Count LESmh dadeaktre si uetatdate sates 170 
Dr. Macecowan’s History of the Ante-Christian Settlement of the Jews in China 170 
Mr. J. Micxt1n’s Cruise in the Gulf of Pe-che-li and Leo-tung (China)....... .. 170 

Captain Suzrarp Ossorn on the Formation of Oceanic Ice in the Arctic 
EVE EIONS i aicoiss tied sisvelon ciceiewee seus Mesiaceidaniawers’ssltiacisionicene onatlsoaneamanairenes de daoadgnseee ee Lee 


Captain J. Patiiser on the Course and Results of the British North American 
Exploring Expedition, under his Command in the Years 1857, 1858, 1859... 170 

Dr. Hecror’s Remarks concerning the Climate of the Saskatchewan 
Psi Chirac, cocmawsenacersncncensee sponcerek. sérasheearina ben decddbocEs pAanre Ese sthomdcce i 

Mr. Suxtrvan’s Remarks concerning the Tribes of Indians inhabiting the 
Country examined by the Expedition............000c000 Paaisesepuidcese sapdepae lyse} 

ConsulPetserick on his proposed Journey from Khartum in Upper Egypt to 
meetCaptain Speke on or near the Lake Nyanza of Central Africa.......... « 174 

Dr. J. Raz on the Formation of poe and Ice Action, as observed in the 
RIG SON SHAY, AUG SCLalts <ccecacssaceccsieconsesessestcous cute sigebanorignseeagancor sone ye! 

on the Aborigines of the etic and Sub- Arctic Se of North 
AMICTICA 22-2 00eeers0es neasneiieteiefaeeese=scdnedsessiaais JodOdexcondne SesupoendecdRegapEnNCoC ce atl 


M.R. von Scuztacintweir’s Remarks on some of the Hoa - India and High 
' Asia (in connexion with casts exhibited) ....... wees tie Ross svalocehdussaes dosepastine A Ua. 


Lieutenant Epwarp ScuLaGintWEIT on the Tribes composing the Population 
WE MOLOCCO os... csevscescessscecsensesee PR EERE ROROLOn eC Ne Og cbc aiesieseiie esetens e'seaiisi wae LT 


Col. Tal. P. SHarrner on the Geography of the North Atlantic Telegraph..... 178 


Captain Parker Snow on the Lost Polar Expedition and Possible Recovery of 
its Scientific Documents.........06000000 deatepaaseecoeecuscmatatst|s sponedodeeconuaae .. 180 


Captain M. H. Synee on the Proposed Communication between the Atlantic 
and Pacific, vid British North America.......sssecsssecseeresereees aonebens Succepac tsi 


M. Prerre ve Tcuiuatcuer on the Geographical Distribution of Plants in 
PSSIDM NL Glucnseveadiecdsicndesttineceshcae(seseoucdsiscseeahtedaverweesneci 6008903050 0s <6) LOM 


Mr. Tuomas Wricut on the Excavations on the site of the Roman City of 
DaRrPeENOP ACM LOXCLEL cE cncesspecocsiaveradik vedevsnacausagtessaccedepersscsaedsevicrecst LOL 


STATISTICAL SCIENCE. 
Opening Address by Nassau W. Senior, M.A., President of the Section ...... 182 


Rev. J. Boorn on the True Principles of an Income Tax.......scssceeeeeeeeeceeees 184 
Miss Mary Carpenter on Educational Help from the Government Grant to 

the destitute and neglected children of Great Britain ...... ele dae Wa saates seiosis Scroce, disy:! 
Mr. E. Cuapwick on the Economical Results of Military Drill in Popular 

Schools ..... Muscbemacierua tees amcaee deena aie Foancbobad sph enocenebanee SeoSeugne parece 185 
—-- on the Physiological as well as Psychological Limits to 

_ Mental Labour...... ApeGoadecdd anthseeoubses adoungpsousuanose Fao gaonnodhs osataodatessooaeee 185 

Mr. R. DowbeEn on Local Taxation for Local Purposes .......0ccseecoscscscescerees 191 


Mr. Henry Fawcett, Dr. Wheweill on the Methed of Political Economy...... 191 


————__——. on Co-operative Societies, their Social and Political 
OREIE Ce Ltercemae apart ee metas cacti caine is dis neneaseientiabaslechhisievecescedsdkaepssestaeseseve, 101 


\ 


(Ir. J. J. Fox on the Province of the Statistician ....scsssssussossesssescessseeseerens 1QL 


Xvi CONTENTS. 


Page 
Mr. J. HircuMman on Sanitary Drainage of TOWNS ....cecccsscceveesesceccesesceseeee IQ] 
Mr. E, Jarvis on the System of Taxation prevailing in the United States....... 191 
Dr. MicHELsEN on Serfdom in Russia .......ecssseeeseaseess dadtiwssapesesason seamen ens 191 
Mr. J. M. Mircuet on the Economical History and Statistics of the Her- 
2111 OS aan OOeC DURE Or OnC Ec Daecemoonscccncondadclcsracoccseee ab ibileisjeserata Beasesenenones 191 
Mr. W. Newmarcu on some suggested Schemes of Taxation, and the Difficul- 
ties of them........... sacdawy sie eoeete cote oosemseeete ar Weg Sdasba sac sake sony uetiet eens awereel OF 
Mr. Henry Joun Ker Porrer’s Hints on the best Plan of Cottage for Agri- 
cultural Labourers......... sesgiee Sneed waved siisesaneneutusaceccssesatanmanclescen cee sscsee 194 
Mr. F. Purpy on the Systems of Poor Law Medical Relief...........s.ss000 eevee 195 
Mr. Henry Roserts’s Notes on various efforts to Improve the Domiciliary 
Condition of the Labouring Classes.......ssssscseesseeneenenees ce sveepeaet SRA (61D) 
MECHANICAL SCIENCE. 
Mr. P. W. Bartow on the Mechanical Effects of combining Suspension Chains 
and Girders, and the value of the Practical Application of this System (illus- 
trated by a Model) ........+.000+ sbubcleupeccucstesscpcssantwspepecsiuecpeatepeaneseeeroeeee .- 201 
Captain BLAKEEKY on Rited' Cannon’. :-c..1..-cs..0sesesuevecheucatssepmeasstes eevee» 201 
Rey. Dr. Boora ona deep Sea Pressure Gauge, invented by Henry Johnson, Esq. 202 
Earl of CarrHness on Road Locomotives...........ceseecessescecesessceves <onscouscsss (20 
Mr. E. Cowprr’s New Mode of obtaining a Blast of very High Temperature 
inthe) ManulactareOlUrOns..5essdenceereoes ores s<ciesnecvacsyses er enewepeerene veoeee 204 
Mr. Jonn Exper on the Cylindrical Spiral Boiler ............sssecessssssveeeees vases 204 
Mr. Wriitam Farrparrn on the Density of Saturated Steam, and on the Law 
of Expansion of Superheated Steam <.ccc.c sic. cc scccceccacsevcecsscassccccccads sseene 210 
Mr. Joun FisHEr on any Atmospheric Washing Machine........++sessessesseee vee 210 


Mr. Witt1am Frovupse on Giffard’s Injector for Feeding Boilers..,.........0.026. 211 
Mr. Watter Hatt on a Process for Covering Submarine Wires with India- 


rubber for Telegraphic purposes...... sis nics sins oes anenes eas const ainecbaspeepenes ALE 211 
Professor Hennessy’s Suggestions relative to Inland Navigation ....se...ss.00. 211 
Mr. Caxucott Rer.ty on the Longitudinal Stress of the Plate Girder........... - 212 
Dr. B. W. Ricwarpson on Suggestions for an Electro-Magnetic Railway 

IBTGak'. 35,0. ciaspssncua sehen «yeu ce ngals Memeo cep = peer esaa topeset> saaeeienges saveeumnsr sass tenes 212 


Mr. S. W. Srtver on the Character and Comparative Value of Gutta Percha . 
and India-rubber employed as Insulators for Subaqueous Telegraphic Wires. 212 


Mr. W. Simons on Improvements in Iron Shipbuilding ........-2+...ccceeeseseeeaes 212 
Admiral Tayztor’s Novel Means to lessen the frightful Loss of Life round 
our exposed Coasts by rendering the Element itself an Inert Barrier against 
the Power of the Sea; also a Permanent Deep-water Harbour of Refuge by 
Artificial Bars........... apie exp tie «codes eccipaess lessens ces as ae see dniincesse sae es ana. anaes 215 


Mr. G. F. Train on Street Railways as used in the United States, illustrated 
by a Model of a Tramway and Car, or Omnibus capable of conveying sixty 


DETSODS ..000.cscccseseusccesss acaideswusiaselcmavelcchenictsncedae’sveasian anes esac usanvetusanees 215 
Messrs. WERNER and C. W. S1emEens on a Mode of covering Wires with 
India-ribber... 0. sscccesse jap teaweasssdaneeas pastes anecanes Rasen sGece Nene Catone spaeh pce, ua 
APPENDIX. 
PHYSIOLOGY. 


/ 


Professor J. H. Consett on the Deglutition of Alimentary Fluids ....00000. 21°» 


/ 


/ 


OBJECTS AND RULES 


OF 


THE ASSOCIATION. 


— i 


OBJECTS. 


Tue Assocration contemplates no interference with the ground occupied by 
other Institutions. Its objects are,—To give a stronger impulse and a more 
systematic direction to scientific inquiry,—to promote the intercourse of those 
who cultivate Science in different parts of the British Empire, with one an- 
other, and with foreign philosophers,—to obtain a more general attention to 
the objects of Science, and a removal of any disadvantages of a public kind 
which impede its progress. 
RULES, 


ADMISSION OF MEMBERS AND ASSOCIATES. 


All Persons who have attended the first Meeting shall be entitled to be- 
come Members of the Association, upon subscribing an obligation to con- 
form to its Rules. 

The Fellows and Members of Chartered Literary and Philosophical So- 
cieties publishing Transactions, in the British Empire, shall be entitled, in 
like manner, to become Members of the Association. 

The Officers and Members of the Councils, or Managing Committees, of 
Philosophical Institutions, shall be entitled, in like manner, to become Mem- 
bers of the Association. 

All Members of a Philosophical Institution recommended by its Council 
or Managing Committee, shall be entitled, in like manner, to become Mem- 
bers of the Association. 

Persons not belonging to such Institutions shall be elected by the General 
Committee or Council, to become Life Members of the Association, Annual 
Subscribers, or Associates for the year, subject to the approval of a General 
Meeting. 

COMPOSITIONS, SUBSCRIPTIONS, AND PRIVILEGES. 

Lire Memprrs shall pay, on admission, the sum of Ten Pounds. They 
shall receive gratuitously the Reports of the Association which may be pub- 
lished after the date of such payment. They are eligible to all the offices 
of the Association. 

Anwnuat Susscrisrrs shall pay, on admission, the sum of Two Pounds, 
and in each following year the sum of One Pound. They shall receive 
gratuitously the Reports of the Association for the year of their admission 
and for the years in which they continue to pay without intermission their 
Annual Subscription. By omitting to pay this Subscription in any particu- 
lar year, Members of this class (Annual Subscribers) lose for that and all 
_ future years the privilege of receiving the volumes of the Association gratis : 
but they may resume their Membership and other privileges at any sub- 
sequent Meeting of the Association, paying on each such occasion the sum of 
One Pound. They are eligible to all the Offices of the Association. 

Associates for the year shall pay on admission the sum of One Pound. 
They shall not receive gratuitously the Reports of the Association, nor be 
eligible to serve on Committees, or to hold any office. i 

1860. 


XVIil RULES OF THE ASSOCIATION. 


The Association consists of the following classes :— 

1, Life Members admitted from 1831 to 1845 inclusive, who have paid 
on admission Five Pounds as a composition. 

2. Life Members who in 1846, or in subsequent years, have paid on ad- 
mission Ten Pounds as a composition. 

_8. Annual Members admitted from 1831 to 1839 inclusive, subject to the 
payment of One Pound annually. [May resume their Membership after in- 
termission of Annual Payment. | 

4. Annual Members admitted in any year since 1859, subject to the pay- 
ment of Two Pounds for the first year, and One Pound in each following 
year. [May resume their Membership after intermission of Annual Pay- 
ment. ] 

5. Associates for the year, subject to the payment of One Pound. 

6. Corresponding Members nominated by the Council. 

And the Members and Associates will be entitled to receive the annual 
volume of Reports, gratis, or to purchase it at reduced (or Members’) price, 
according to the following specification, viz. :— 

1. Gratis.—Old Life Members who have paid Five Pounds as a compo- 
sition for Annual Payments, and previous to 1845 a further 
sum of Two Pounds as a Book Subscription, or, since 1845, a 
further sum of Five Pounds. 

New Life Members who have paid Ten Pounds as a com- 
position. 

Annual Members who have not intermitted their Annual Sub- 
scription. 

2. At reduced or Members’ Prices, viz. two-thirds of the Publication 
Price.—Old Life Members who have paid Five Pounds as a 
composition for Annual Payments, but no further sum as a 
Book Subscription. : 

Arnual Members, who have intermitted their Annual Subscrip- 
tion. 

Associates for the year. [Privilege confined to the volume for 
that year only. ] 

3. Members may purchase (for the purpose of completing their sets) any 
of the first seventeen volumes of Transactions of the Associa- 
tion, and of which more than 100 copies remain, at one-third of 
the Publication Price. Application to be made (by letter) to 
Messrs. Taylor & Francis, Red Lion Court, Fleet St., London. 

Subscriptions shall be received by the Treasurer or Secretaries. 


MEETINGS. 

The Association shall meet annually, for one week, or longer. The place 
of each Meeting shall be appointed by the General Committee at the pre- 
vious Meeting; and the Arrangements for it shall be entrusted to the Offi- 
cers of the Association, 

GENERAL COMMITTEE. 

The General Committee shall sit during the week of the Meeting, or 
longer, to transact the business of the Association. It shall consist of the 
following persons :— 

1. Presidents and Officers for the present and preceding years, with 
authors of Reports in the Transactions of the Association. 

2. Members who have communicated any Paper to a Philosophical Society, 
which has been printed in its Transactions, and which relates to such subjects 
as are taken into consideration at the Sectional Meetings of the Association. 


RULES OF THE ASSOCIATION. X1X 


3. Office-bearers for the time being, or Delegates, altogether not exceed- 
ing three in number, from any Philosophical Society publishing Transactions. 

4, Office-bearers for the time being, or Delegates, not exceeding three, 
from Philosophical Institutions established in the place of Meeting, or in any 
place where the Association has formerly met. 

5, Foreigners and other individuals whose assistance is desired, and who 
are specially nominated in writing for the Meeting of the year by the Presi- 
dent and General Secretaries. 

6. The Presidents, Vice-Presidents, and Secretaries of the Sections are 
ex-officio members of the General Committee for the time being. 


SECTIONAL COMMITTEES. 

The General Committee shall appoint, at each Meeting, Committees, con- 
sisting severally of the Members most conversant with the several branches 
of Science, to advise together for the advancement thereof. 

_ The Committees shall report what subjects of investigation they would 
particularly recommend to be prosecuted during the ensuing year, and 
brought under consideration at the next Meeting. 

The Committees shall recommend Reports on the state and progress of 
particular Sciences, to be drawn up from time to time by competent persons, 
for the information of the Annual Meetings. 


: COMMITTEE OF RECOMMENDATIONS. 

The General Committee shali appoint at each Meeting a Committee, which 
shall receive and consider the Recommendations of the Sectional Committees, 
and report to the General Committee the measures which they would advise 
to be adopted for the advancement of Science. 

All Recommendations of Grants of Money, Requests for Special Re- 
searches, and Reports on Scientific Subjects, shall be submitted to the Com- 
mittee of Recommendations, and not taken into consideration by the General 
Committee, unless previously recommended by the Committee of Recom- 
mendations. 

LOCAL COMMITTEES. 

Local Committees shall be formed by the Officers of the Association to 
assist in making arrangements for the Meetings. 

Local Committees shall have the power of adding to their numbers those 
Members of the Association whose assistance they may desire. 


OFFICERS. 


A President, two or more Vice-Presidents, one or more Secretaries, and a 
Treasurer, shall be annually appointed by the General Committee. 


: COUNCIL. 

In the intervals of the Meetings, the affairs of the Association shall be 
managed by a Council appointed by the General Committee. - The Council 
may also assemble for the despatch of business during the week of the 
Meeting. 

PAPERS AND COMMUNICATIONS. 

The Author of any paper or communication shall be at liberty to reserve 

his right of property therein. 
ACCOUNTS. 
The Accounts of the Association shall be audited annually, by Auditors 


appointed by the Meeting. ae 


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MEMBERS OF THE COUNCIL. 


XXV 


II. Table showing the Names of Members of the British Association who 
have served on the Council in former years. 


Aberdeen, Earl of, LL.D., K.G., K.T., 
F.R.S. (dec‘). 

Acland, Sir Thomas D., Bart., F.R.S. 

Acland, Professor H. W., M.D., F.R.S. 

Adams, J. Couch, M.A., F.R.S. 

Adamson, John, Esq., F.L.S. 

Ainslie, Rev. Gilbert, D.D., Master of Pem- 
broke Hall, Cambridge. 

Airy,G.B.,D.C.L.,F.R.S.,Astronomer Royal. 

Alison, Professor W. P.,M.D.,F.R.S.E.(dec*). 

Allen, W. J. C., Esq. 

Anderson, Prof. Thomas, M.D. 

Ansted, Professor D. T., M.A., F.R.S. 

Argyll, George Douglas, Duke of, F.R.S. 

Arnott, Neil, M.D., F.R.S. 

Ashburton, William Bingham, Lord, D.C.L, 

Atkinson, Rt. Hon. R.,Lord Mayor of Dublin. 

Babbage, Charles, Esq., M.A., F.R.S. 

Babington, Professor CO. C., M.A., F.R.S. 

Baily, Francis, Esq., F.R.S. (deceased). 

Baines, Rt. Hon. M.T., M.A., M.P. (dec*). 

Baker, Thomas Barwick Lloyd, Esq. 

Balfour, Professor John H., M.D., F.B.S. 

Barker, George, Hsq., F.R.S. (deceased). 

Beamish, Richard, Hsq., F.R.8. 

Bell, Professor Thomas, Pres. L.S., F.R.S. 

Beechey, Rear-Admiral, F.R.S. (deceased). 

Bengough, George, Esq. 

Bentham, George, Esq., F.LS. 

Biddell, George Arthur, Esq. 

Bigge, Charles, Esq. 

Blakiston, Peyton, M.D., F.R.8. 

Boileau, Sir John P., Bart., F.R.S. 

Boyle, Rt.Hon. D., Lord Justice-Gen!. (dec*). 

Brady,The Rt. Hon. Maziere, M.R.1.A., Lord 
Chancellor of Ireland. 

Brand, William, Esq. 

Breadalbane, John, Marquis of, K.T., F.R.S. 

Brewster, Sir David, K.H., D.C.L., LL.D., 
F.R.S., Principal of the University of 
Edinburgh. 

Brisbane, General Sir Thomas M., Bart., 
K.C.B., G.C.H., D.C.L., F.R.S. (dec*). 

Brodie, Sir B. C., Bart., D.C.L., Pres. B.S. 

Brooke, Charles, B.A., F.R.S. 

Brown, Robert, D.C.L., F.R.S. (deceased). 

Brunel, Sir M. I., F.R.S. (deceased). 

Buckland, Very Rev. William, D.D., F.RB.8., 
Dean of Westminster (deceased). 

Bute, John, Marquis of, K.'T. (deceased). 

Carlisle, George Will. Fred., Earl of, F.R.S. 

Carson, Rey. Joseph, F.T.C.D. 

Cathcart, Lt.-Gen., Earlof, K.C.B., F.R.S.E. 
(deceased). 

Chalmers, Rev. T., D.D. (deceased). 

Chance, James, Esq. 

Chester, John Graham, D.D., Lord Bishop of. 

Christie, Professor 8. H., M.A., F.R.S. 

Clare, Peter, Esq., F.R.A.S. (deceased). 

Clark, Rev. Prof., M.D., F.R.S. (Camtridge.) 

Clark, Henry, M.D. 

Clark, G. T., Esq. 

Clear, William, Esq. (deceased), 


Clerke, Major 8., K.H., R.E., F.R.S. (dec*). 

Clift, William, Hsq., F’.R.S. (deceased). 

Close, Very Rev. F., M.A., Dean of Carlisle. 

Cobbold, John Chevalier, Esq., M.P. 

Colquhoun, J. C., Esq., M.P. (deceased). 

Conybeare, Very Rev. W. D., Dean of Llan- 
daff (deceased). 

Cooper, Sir Henry, M.D. 

Corrie, John, Esq., F.R.S. (deceased). 

Crum, Walter, Esq., F.R.S. 

Currie, William Wallace, Esq. (deceased). 

Dalton, John, D.C.L., F.R.S. (deceased). 

Daniell, Professor J. F., F.R.S. (deceased). 

Dartmouth, William, Earl of, D.C.L., F.R.S. 

Darwin, Charles, Esq., M.A., F.R.S. 

Daubeny, Prof. Charles G. B., M.D., F.R.8. 

DelaBeche, Sir H. T., C.B., F.R.S8., Director- 
Gen. Geol. Surv. United Kingdom (dec‘). 

De la Rue, Warren, Ph.D., F.R.S. 

Devonshire, William, Duke of, M.A., F.R.S. 

Dickinson, Joseph, M.D., F.R.S. 

Dillwyn, Lewis W., Hsq., F.R.S. (deceased). 

Drinkwater, J. E., Esq. (deceased). 

Ducie, The Earl, F.R.S. 

Dunraven, The Earl of, F.R.S. 

Egerton, Sir P, de M. Grey, Bart., M.P., 
E.R.S 


Eliot, Lord, M.P. 

Ellesmere, Francis, Earl of, F.G.8. (dec*). 

Enniskillen, William, Earl of, D.C.L., F.R.S, 

Estcourt, T. G. B., D.C.L. (deceased). 

Fairbairn, William, LL.D., C.E., F.R.S. 

Faraday, Professor, D.C.L., F.R.S. 

FitzRoy, Rear Admiral, F.R.S. 

Fitzwilliam, The Earl, D.C.L., F.R.S. (dec*). 

Fleming, W., M.D. 

Fletcher, Bell, M.D. 

Foote, Lundy E., Esq. 

Forbes, Charles, Esq. (deceased). 

Forbes, Prof. Edward, F.R.S. (deceased). 

Forbes, Prof. J. D., F.R.S., Sec. R.S.E. 

Fox, Robert Were, Esq., F.R.8. 

Frost, Charles, F.S.A. 

Fuller, Professor, M.A. 

Gassiot, John P., Esq., F.R.S. 

Gilbert, Davies, D.C.L., F.R.S. (deceased). 

Gourlie, William, Esq. (deceased). 

Graham, T., M.A., F.R.S., Master of the Mint. 

Gray, John E., Esq., Ph.D., F.R.S. 

Gray, Jonathan, Esq. (deceased). 

Gray, William, Esq., F.G.S. 

Green, Prof. Joseph Henry, D.C.L., F.R.S. 

Greenough, G. B., Esq., ¥.R.S. (deceased). 

Griffith, Sir R. Griffith, Bt., LL.D., M.R.1.A. 

Grove, W. R., Hsq., M.A., F-.R.S. 

Hallam, Henry, Esq., M.A., F.R.S. (dec*). 

Hamilton, W. J., Esq., F.R.S8., For. Sec. G.S. 

Hamilton, Sir Wm. R., LL.D., Astronomer 
Royal of Ireland, M.R.LA., F.R.AS. 

Hancock, W. Neilson, LL.D. 

Harcourt, Rev. Wm. Vernon, M.A., F.R.S. 

Hardwicke, Charles Philip, Earl of, F.R.S. 

Harford, J. §., D.C.L., F.R.S. ; 


= > 
XXV1 


Harris, Sir W. Snow, F.R.S. 

Harrowby, The Earl of, F.R.S8. 

Hatfeild, William, Esq., F.G.S. (deceased). 

Henry, W. C., M.D., F.R.S. [Col., Belfast. 

Henry, Rev. P.S., D.D., President of Queen’s 

Henslow, Rey. Professor, M.A., F.L.8. (dec®). 

Herbert, Hon. and Very Rey. Wm., LL.D., 
F.L.S., Dean of Manchester (dec*). 

Herschel,Sir John F.W., Bart.,D.C.L., F.R.S. 

Heywood, Sir Benjamin, Bart., F.R.S. 

Heywood, James, Esq., F.R.S. 

Hill, Rev. Edward, M.A., F.G.S. 

Hincks, Rey. Edward, D.D., M.R.I.A. 

Hincks, Rev. Thomas, B.A. 

Hinds,8., D.D., late Lord Bishop of Norwich. 
(deceased). 

Hodgkin, Thomas, M.D. 

Hodgkinson, Professor Eaton, F.R.S. 

Hodgson, Joseph, Esq., F.R.S. 

Hooker, Sir William J., LL.D., F.R.S. 

Hope, Rev. F. W., M.A., F.R.S. 

Hopkins, William, Esq., M.A., F.R.S. 

Horner, Leonard, Esq., F.R.S., F.G.S8. 

Hovenden, V. F., Esq., M.A. 

Hugall, J. W., Esq. 

Hutton, Robert, Esq., F.G.S. 

Hutton, William, Esq., F.G.S. 

Ibbetson,Capt.L.L. Boscawen, K.R.E.,F.G.S. 

Inglis, Sir R. H., Bart., D.C.L., M.P. (dec*). 

Inman, Thomas, M.D. 

Jacobs, Bethel, Esq. 

Jameson, Professor R., F.R.S. (deceased). 

Jardine, Sir William, Bart., F.R.S.E. 

Jeffreys, John Gwyn, Esq., F.R.S. 

Jellett, Rev. Professor. 

Jenyns, Rey. Leonard, F.L.S. 

Jerrard, H. B., Esq. 

Johnston, Right Hon. William, late Lord 
Provost of Edinburgh. 

Johnston, Prof.J. F. W.,M.A., F.R.S. (dec). 

Keleher, William, Esq. (deceased). 

Kelland, Rey. Professor P., M.A. 

Kildare, The Marquis of. 

Lankester, Edwin, M.D., F.R.S. 

Lansdowne, Hen., Marquisof, D.C.L.,F.R.S. 

Larcom, Major, R.E., LL.D., F.R.S. 

Lardner, Rey. Dr. (deceased). 

Lassell, William, Esq., F.R.S. L. & E. 

Latham, R. G., M.D., F.R.S. 

Lee, Very Rey. John, D.D., F.R.S.E., Prin- 
cipal of the University of Edinburgh. 
(deceased). 

Lee, Robert, M.D., F.R.S. 

Lefevre, Right Hon. Charles Shaw, late 
Speaker of the House of Commons. 

Lemon, Sir Charles, Bart., F.R.S. 

Liddell, Andrew, Esq. (deceased). 

Lindley, Professor John, Ph.D., F.R.S. 

Listowel, The Earl of. [Dublin (dec*). 

Lloyd, Rey. B., D.D., Provost of Trin. Coll., 

Lloyd, Rev. H., D.D., D.C.L., F.R.S. L.&E. 

Londesborough, Lord, F.R.S. (deceased). 

Lubbock, Sir John W., Bart., M.A., F.R.S. 

Luby, Rev. Thomas. 

Lyell, Sir Charles, M.A., F.R.S. 

MacCullagh, Prof., D.C.L., M.R.1.A. (dec*). 


REPORT— 1860. 


MacDonnell, Rev. R., D.D., M.R.LA., Pro- 
vost of Trinity College, Dublin. 

Macfarlane, The Very Rev. Principal. (dec*). 

MacGee, William, M.D. 

MacLeay, William Sharp, Esq., E.L.S. 

MacNeill, Professor Sir John, F.R.S. 

Malahide, The Lord Talbot de. 

Malcolm, Vice-Ad. Sir Charles, K.C.B. (dec*). 

Maltby, Edward, D.D., F.R.S., late Lord 
Bishop of Durham (deceased). 

Manchester, J. P. Lee, D.D., Lord Bishop of. 

Marshall, J. G., Esq., M.A., F.G.8. 

May, Charles, Esq., F.R.A.S8. 

Meynell, Thomas, Esq., F.L.S. 

Middleton, Sir William F. F., Bart. 

Miller, Professor W. A., M.D., F.R.S. 

Miller, Professor W. H., M.A., F.RB.S. 

Moillet, J. D., Esq. (deceased). 

Milnes, R. Monckton, Esq., D.C.L., M.P. 

Moggridge, Matthew, Esq. 

Monteagle, Lord, F.R.8. 

Moody, J. Sadleir, Esq. 

Moody, T. H. C., Esq. 

Moody, T. F., Esq. 

Morley, The Earl of. 

Moseley, Rey. Henry, M.A., F.R.S. 

Mount-Edgecumbe, ErnestAugustus, Earl of. 

Murchison, Sir Roderick I.,G.C. St.8., F.R.S. 

Neill, Patrick, M.D., F.R.S.E. 

Nicol, D., M.D. 

Nicol, Professor J., F.R.S.E., F.G.S. 

Nicol, Rey. J. P., LL.D. 

Northampton, Spencer Joshua Alwyne, Mar- 
quis of, V.P.R.S. (deceased). 

Northumberland, Hugh, Duke of, K.G.,M.A., 
F.R.S. (deceased). 

Ormerod, G. W., Hsq., M.A., F.G.S. 

Orpen, Thomas Herbert, M.D. (deceased). 

Orpen, John H., LL.D. 

Osler, Follett, Esq., F.R.S. 

Owen, Professor Richd.,M.D., D.C.L.,F.R.S. 

Oxford, Samuel Wilberforce, D.D., Lord 
Bishop of, F.R.S., F.G.S. 

Palmerston, Viscount, G.C.B., M.P. 

Peacock, Very Rey. G., D.D., Dean of Ely, 
F.R.S. (deceased). : 

Peel, Rt.Hon.Sir R.,Bart.,M.P.,D.C.L.(dec*). 

Pendaryes, E. W., Esq., F.R.S. (deceased). 

Phillips, Professor John, M.A., LL.D.,F.R.S. 

Pigott, The Rt. Hon. D. R., M.R.1.A., Lord 
Chief Baron of the Exchequer in Ireland. 

Porter, G. R., Esq. (deceased). 

Portlock, General, R.E., F.R.S. 

Powell, Rev. Professor, M.A., F.R.S. (dec*). 

Price, Rey. Professor, M.A., F.R.S. 

Prichard, J. C., M.D., F.R.S. (deceased). 

Ramsay, Professor William, M.A. 

Ransome, George, Esq., F.L.S. 

Reid, Maj.-Gen. Sir W., K.C.B., R.E., F.B.S. 
(deceased). 

Rendlesham, Rt. Hon. Lord, M.P. 

Rennie, George, Hsq., F.R.S. 

Rennie, Sir John, F.R.S. 

Richardson, Sir John, M.D., C.B., F.R.S. 

Richmond, Duke of, K.G., F.R.S. (dec*). 


Ripon, Earl of, F.R.G.S. 


MEMBERS OF THE COUNCIL. 


Ritchie, Rev. Prof., LL.D., F.R.S. (dec*). 

Robinson, Capt., R.A. 

Robinson, Rev. J., D.D. 

Robinson, Rey. T. R., D.D., F.R.AS. 

Robison, Sir John, Sec.R.S. Edin. (deceased). 

Roche, James, Esq. 

Roget, Peter Mark, M.D., F.R.S. 

Ronalds, Francis, F.R.S. 

Rosebery, The Harl of, K.T., D.C.L., F.R.S. 

Ross, Rear-Ad. Sir J.C.,R.N., D.C.L., F.B.S. 

Rosse, Wm., Earl of, M.A., F.R.S., M.R.LA. 

Royle, Prof. John F., M.D., F.R.S. (dec). 

Russell, James, Esq. (deceased). 

Russell, J. Scott, Esq., F.R.S. [V.P.R.8. 

Sabine, Maj.-General, R.A., D.C.L., Treas. & 

Sanders, William, Esq., F.G.S. 

Scoresby, Rev. W., D.D., F.R.S. (deceased). 

Sedgwick, Rev. Prof. Adam, M.A., F.R.S. 

Selby, Prideaux John, Esq., F.R.S.E. 

Sharpey, Professor, M.D., Sec.R.8. 

Sims, Dillwyn, Esq. 

Smith, Lieut.-Colonel C. Hamilton, F.R.S. 
(deceased). 

Smith, James, F.R.S. L. & E. 

Spence, William, Esq., F.R.S. (deceased). 

Stanley, Edward, D.D., F.R.S., late Lord 
Bishop of Norwich (deceased). 

Staunton, Sir G. T., Bt., M.P., D.C.L., F.R.S. 

St. David’s, C.Thirlwall,D.D.,LordBishop of. 

Stevelly, Professor John, LL.D. 

Stokes, Professor G. G., Sec.R.S. 

Strang, John, Esq., LL.D. 

Strickland, Hugh E., Esq., F'.R.S. (deceased). 

Sykes, Colonel W. H., M.P., F.R.S. 

Symonds, B. P., D.D., Warden of Wadham 
College, Oxford. 

Talbot, W. H. Fox, Esq., M.A., F.R.S. 

Tayler, Rev. John James, B.A. 

Taylor, John, Esq., F.R.S. 

Taylor, Richard, Hsq., F.G.S. 


XXVil 


Thompson, William, Hsq., F.L.S. (deceased). 

Thomson, A., Esq. 

Thomson, Professor William, M.A., F.R.S. 

Tindal, Captain, R.N. (deceased). 

Tite, William, Esq., M.P., F.R.S. 

Tod, James, Esq., F.R.S.E. 

Tooke, Thomas, F.R.S. (deceased). 

Traill, J. S., M.D. (deceased). 

Turner, Edward, M.D., F.R.S. (deceased). 

Turner, Samuel, Esq., F.R.S., F.G.8. (dec*). 

Turner, Rev. W. 

Tyndall, Professor, F.R.S. 

Vigors, N. A., D.C.L., F.L.S. (deceased). 

Vivian, J. H., M.P., F.R.S. (deceased). 

Walker, James, Esq., F.R.S. 

Walker, Joseph N., Esq., F.G-S. 

Walker, Rev. Professor Robert, M.A., F.R.S. 

Warburton, Henry, Hsq.,.M.A., F.R.S.(dec*). 

Ward, W. Sykes, Esq., F.C.S. 

Washington, Captain, R.N., F.R.S. 

Webster, Thomas, M.A., F.R.S. 

West, William, Esq., F.R.S. (deceased). 

Western, Thomas Burch, Esq. 

Wharncliffe, John Stuart, Lord, F.R.S.(dec*). 

Wheatstone, Professor Charles, F.R.S. ’ 

Whewell, Rey. William, D.D., F.R.S., Master 
of Trinity College, Cambridge. 

White, John F., Esq. 

Williams, Prof. Charles J. B., M.D., F.R.8. 

Willis, Rev. Professor Robert, M.A., F.R.S. 

Wills, William, Esq., ¥.G.S. (deceased). 

Wilson, Thomas, EHsq., M.A. 

Wilson, Prof. W. P. 

Winchester, John, Marquis of. 

Woollcombe, Henry, Esq., F.S.A. (deceased). 

Wrottesley, John, Lord, M.A., F.R.S. 

Yarborough, The Ear! of, D.C.L. 

Yarrell, William, Esq., F.L.S. (deceased). 

Yates, James, Esq., M.A., F.R.S. 

Yates, J. B., Esq., F.S.A., F.R.G.S. (dec*). 


OFFICERS AND COUNCIL, 1860-61. 


TRUSTEES (PERMANENT). 


51k RopERIcK I. MurcuIson, G.C.St.S., F.R.S. JOHN TAYLOR, Esq., F.R.S, 
Major-General EDWARD SABINE, R.A., D.C.L., Treas. & V.P.R.S. 
PRESIDENT. 


THE LORD WROTTESLEY, M.A., V.P.R.S, F.R.A.S, 


VICE-PRESIDENTS. 
The EArt oF DERBY, P.C., D.C.L., Chancellor of | CHarLES G. B. DAuBENy, LL.D., M.D., F-.R.S., 


the University of Oxford. F.L.S., F.G.S., Professor of Botany in the Uni- 
The Rey. F, JEUNE, D.D., Vice-Chancellor of the versity of Oxford. 

University of Oxford. HENRY W. ACLAND, M.D., D.C.L., F.R.S., Regius 
The DuKE oF MARLBOROUGH, D.C.L. Professor of Medicine in the University of Ox- 
The EARL OF Rosse, K.P., M.A., F.R.S., F.R.A.S. ford. 

The Lorp BIsHoP OF OXFORD, F.R.S. WILLIAM F. Donkin, Esq., M.A., F.R.S., Savilian 
The Very Rev. H. G. LippELL, D.D., Dean of Professor of Astronomy in the University of Ox- 
Christ Church, Oxford. ford. 


PRESIDENT ELECT. 
WILLIAM FAIRBAIRN, Esq., LL.D., C.E., F.R.S, 


VICE-PRESIDENTS ELECT. 
The EARL oF ELLESMERE, F.R.G.S. JAMES ASPINALL TURNER, Esq., M.P. 
The Lorp STANLEY, M.P., D.C.L., F.R.G.S. JAMES PRESCOTT JOULE, Esq., LL.D., F.R.S., Pre- 
The Lorp BisHop OF MANCHESTER, D.D., F.R.8., sident of the Literary and Philosophical Society 
.G.S. of Manchester. 
Sir Poitrp DE MALpas GREY EGERTON, Bart., | Eaton HopeKtnson, Esq., F.R.S., M.R.I.A., 


M.P., F.R.S., F.G.S. M.I.C.E., Professor of the Mechanical Principles 
Sir Bensamin HEywoop, Bart., F.R.S, of Engineering in University College, London. 
THOMAS BAazLEY, Esq., M.P. JOSEPH WHITWORTH, Esq., F'.R.S., M.I.C.E. 


LOCAL SECRETARIES FOR THE MEETING AT MANCHESTER. 
ROBERT DUKINFIELD DARBISHIRE, Esq., B.A., F.G.S., Brown Street, Manchester, 
ALFRED NEILD, at Mayfield, Manchester. 

ARTHUR RANSOME, Esq., M.A., St. Peter’s Square, Manchester. 
Professor HENRY ENFIELD Roscor, B.A., Owens College, Manchester. 
LOCAL TREASURER FOR THE MEETING AT MANCHESTER. 
ROBERT PHILIPS GREG, Esq., F.G.S., Manchester. 


ORDINARY MEMBERS OF THE COUNCIL. 


BaBinGTon, C. C., M.A., F.R.S. | GLADSTONE, Dr. J. H., F.R.S. SHARPEY, Professor, Sec. B.S. 
BELL, Prof. T., Pres. L.S., F.R.S. | GRovE, WILLIAM R., F.R.S. SpPorriswoopr, W., M.A., F.R.S8, 
Bropik, Sir BENJAMIN C., Bart., | HoRNER, LEONARD, F.R.S. Sykes, Colonel W. Fa es 
D.C.L., Pres. R.8. Huron, Ropert, F.G.S. FE.R.S. 
8. 


H. 
DE LA RUE, WARREN, Ph.D., | LYELL, Sir C., D.C.L., F.R.S. Tire, WILLIAM, M.P., F. 

E.R.S. MILLER, Prof.W. A., M.D., F.R.S. | TyNDALL, Professor, F.R 
FirzRoy, Rear Admiral, F.R.S. PorTLOCK, General, R.E., F.R.S. | WEBSTER, THOMAS, F.R. 
GALTON, FRANCIS, F.G.S. PRICE, Rey. Prof., M.A., F.R.S. WILLIs, Rey. Prof., M.A., F.R.S. 
Gassior, JOHN P., F.R.S. 


EX-OFFICIO MEMBERS OF THE COUNCIL. 


The President and President Elect, the Vice-Presidents and Vice-Presidents Elect, the General and 
Assistant-General Secretaries, the General Treasurer, the Trustees, and the Presidents of former years, 
yiz.—Rev. Professor Sedgwick. The Marquis of Lansdowne. The Duke of Devonshire. Rey. W. V. Har- 
court. The Marquis of Breadalbane. Rey. W. Whewell, D.D. The Earl of Rosse. Sir John F, W. 
Herschel, Bart. Sir Roderick I. Murchison. The Rey. T. R. Robinson, D.D. Sir David Brewster. 
G. B. Airy, Esq., the Astronomer Royal. General Sabine. William Hopkins, Esq., LL.D. The Earl of 
Harrowby. The Duke of Argyll. Professor Daubeny, M.D. The Rev. H. Lloyd, D.D. Professor 
Owen, M.D., D.C.L. His Royal Highness The Prince Consort. 


GENERAL SECRETARY. 
The Rey. ROBERT WALKER, M.A., F.R.S., Professor of Experimental Philosopliy in the University of 
Oxford; Culham Vicarage, Abingdon. 
ASSISTANT-GENERAL SECRETARY. 


JouN PHILLIPS, Esq., M.A., LL.D., F.R.S., F.G.S., Professor of Geology in the University of Oxford ; 
Museum House, Oxford. 


CENERAL TREASURER. 
JouHN TAYLOR, Esq., F.R.S., 6 Queen Street Place, Upper Thames Street, London. 
LOCAL TREASURERS. 


R. 
8. 
8 


William Gray, Esq., F.G.S., York. John Gwyn Jeffreys, Esq., F.R.S., Swansea. 
C. C. Babington, Esq., M.A., F.R.S., Cambridge. J. B. Alexander, Ksq., ong 

William Brand, Esq., Edinburgh. Robert Patterson, Esq., M.R.LA., Belfast. 
John H. Orpen, LL.D., Dublin. Edmund Smith, Esq., Hull. 

William Sanders, Esq., F.G.S., Bristol. Richard Beamish, Esq., F.R.S., Cheltenham. 
Robert M‘Andrew, Esq., F.R.S., Liverpool. John Metcalfe Smith, Esq., Leeds. 

W. R. Wills, Esq., Birmingham. John Angus, Esq., Aberdeen. 

Professor Ramsay, M.A., Glasqow. Rey. John Griffiths, M.A., Oxford. 


Robert P. Greg, Esq., F.G.S., Manchester. 
AUDITORS. 
Robert Hutton, Esq. Dr. Norton Shaw. John P. Gassiot, Esq. 


OFFICERS OF SECTIONAL COMMITTEES. XX1X 


OFFICERS OF SECTIONAL COMMITTEES PRESENT AT THE 
ABERDEEN MEETING, 


SECTION A.—-MATHE&MATICS AND PHYSICS. 
President.—Rev. B. Price, M.A., F.R.S., Professor of Natural Philosophy, Oxford. 
Vice- Presidents.—Sir David Brewster, K.H.,D.C.L., F.R.S.; Rev. H. Lloyd, D.D., 
F.R.S., M.R.I.A.; Rev. R. Main, M.A., F.R.S.; Rev. W. Whewell, D.D., F.R.S., 
Hon. M.R.1.A., Master of Trinity College, Cambridge. 
Secretaries.—Professor Stevelly, LL.D.; Rev. T. Rennison, M.A., Fellow of 
Queen’s College; Rev. G. C. Bell, M.A., Fellow of Worcester College. 


SECTION B.—CHEMISTRY AND MINERALOGY, INCLUDING THEIR APPLICATIONS 
TO AGRICULTURE AND THE ARTs. 

President.—B. C. Brodie, Esq., M.A., F.R.S., F.C.S., Professor of Chemistry, 
Oxford. 

Vice- Presidents. —Professor Andrews, M.D., F.R.S., M.R.1.A., F.C.S.; Warren 
De la Rue, Ph.D., F.R.S., F.C.S.; Professor Faraday, D.C.L., F.R.S., F.C.S.; 
Professor Frankland, Ph.D., F.R.S.; Professor W. A. Miller, M.D., F.R.S., F.C.S.; 
Lyon Playfair, C.B., Ph.D., F.R.S., F.C.S. 

Secretaries.—G. D. Liveing, M.A., F.C.S.; A. Vernon Harcourt, Esq., B.A., 
F.C.S., Student of Christ Church; A. B. Northcote, Esq., F.C.S., Queen’s College. 


SECTION C.—GEOLOGY. 

President.,—Rev. A. Sedgwick, M.A., LL.D., F.R.S., F.G.S., Professor of Geology, 
Cambridge. 

Vice-Presidents.—Sir Charles Lyell, LL.D., D.C.L., F.R.S., Hon. M.R.S.E., 
F.G.S.; L. Horner, Pres. G.S., F.R.S.; Major-General Portlock, R.E., LL.D., 
F.R.S., F.G.S. 

Secretaries.—Professor Harkness, F.R.S., F.G.S.; Captain Woodall, M.A., 
F.G.S., Oriel College; Edward Hull, B.A., F.G.S. 


SECTION D.—ZOOLOGY AND BOTANY, INCLUDING PHYSIOLOGY. 
President.—Rev. Professor Henslow, F.L.S., Professor of Botany, Cambridge. 
Vice-Presidents.— Professor Daubeny, M.D., LL.D., F.R.S., F.L.S.; Sir W. Jar- 
dine, Bart., F.R.S.E., F.L.S.; Professor Owen, M.D., LL.D., F.R.S., F.L.S. 

Secretaries.—E. Lankester, M.D., LL.D., F.R.S., F.L.S.; E. Percival Wright, 
M.A., M.B., M.R.ILA., F.L.S.; P. L. Sclater, M.A., F.L.S., Sec. Z.S., C.C.C.; 
W.S. Church, B.A., University College. 


SUB-SECTION D.—PHYSIOLOGICAL SCIENCE. 
President.—George Rolleston, M.D., F.L.S., Professor of Physiology. 
Vice-Presidents.—Professor Acland, M.D., LL.D., F.R.S.; Sir B. Brodie, Bart., 

D.C.L., Pres. R.S.; George Busk, F.R.S.; Dr. Davy, F.R.S. L. & E.; Professor 
Huxley, F.R.S.; W. Sharpey, M.D., Sec. R.S., F.R.S.E. 
Secretaries.—Robert M°Donnell, M.D., M.R.I.A.; Edward Smith, M.D., F.R.S. 


SECTION E.—GEOGRAPHY AND ETHNOLOGY. 

President.—Sir R.I. Murchison, G.C.St.S.,D.C.L., F.R.S., V.P.R.G.S.; Director- 
General of the Geological Survey of the United Kingdom. 

Vice-Presidents.—Lord Ashburton, M.A., F.R.S.; John Crawfurd, Esq., F.R.S., 
Pres. Ethn. Soc.; Francis Galton, Esq., M.A., F.R.S.; Sir J. Richardson, C.B., 
M.D., LL.D., F.R.S., F.R.G.S.; Sir Walter C. Trevelyan, Bart. 

Secretaries.—Norton Shaw, M.D., Sec. R.G.S.; Thomas Wright, M.A., F.S.A.; 
Captain Burrows, R.N., M.A.; Charles Lempriere, D.C.L.; Dr. James Hunt, F.S.A. 


SECTION F.—ECONOMIC SCIENCE AND STATISTICS. 
President.—Nassau W. Senior, M.A., late Professor of Political Economy, Oxford. 
Vice-Presidents.—Sir John P. Boileau, Bart., F.R.S.; James Heywood, F.R.S. ; 

Lord Monteagle, F.R.S.; Monckton Milnes, M.P.; Right Hon. Joseph Napier, 
LL.D., D.C.L.; Sir Andrew Orr; Sir J. Kay Shuttleworth, Bart., F.G.S.; Col. Sykes, 
M.P., F.R.S.; William Tite, Esq., M.P., F.R.S, 


XXX 


REPORT—1860. 


Secretaries.—William Newmarch; Edmund Macrory, M.A.; Rev. J. E. T. 
Rogers, M.A., Magdalen Hall, Tooke Professor of Political Economy, King’s Col- 


lege, London. 


SECTION G.—MECHANICAL SCIENCE. 
President.—W. J. Macquorn Rankine, LL.D., F.R.S., Professor of Engineering, 


Glasgow. 


Vice-Presidents.—J. F. Bateman, F.R.S.; W. Fairbairn, C.E., LL.D., F.R.S. ; 
J. Glynn, F.R.S.; Admiral Moorsom; Sir John Rennie, F.R.S.; Marquis of Stafford, 
M.P.; James Walker, C.E., LL.D., F,.R.S.; Professor Willis, M.A., F.R.S.; 


T. Webster, Q.C., M.A., F.R.S. 


Secretaries,—P. Le Neve Foster, M.A.; Rey. Francis Harrison, M.A.; Henry 


Wright. 


CORRESPONDING MEMBERS. 


Professor Agassiz, Cambridge, Massa- 
chusetts. 
M. Babinet, Paris. 
Dr. A. D. Bache, Washington. 
Professor Bolzani, Kazan, 
Dr. Barth. 
Dr. Bergsma, Utrecht. 
r. P. G. Bond, Cambridge, U.S. 
M. Boutigny (d’Evreux). 
Professor Braschmann, Moscow. 
Dr. Carus, Leipzig. 
Dr. Ferdinand Cohn, Breslau. 
M. Antoine d’Abbadie. 
M. De la Rive, Geneva. 
Professor Dove, Berlin. 
Professor Dumas, Paris. 
Dr. J. Milne-Edwards, Paris. 
Professor Ehrenberg, Berlin. 
Dr. Eisenlohr, Carlsruhe. 
Professor Encke, Berlin. 
Dr. A. Erman, Berlin. 
Professor Esmark, Christiania. 
Prof. A. Favre, Geneva. 
Professor G. Forchhammer, Copenhagen. 
M. Léon Foucault, Paris. 
Prof. E. Fremy, Paris. 
M. Frisiani, Milan. 
Dr. Geinitz, Dresden. 
Professor Asa Gray, Cambridge, U.S. 
Professor Henry, Washington, U.S. 
Dr. Hochstetter, Vienna. 
M. Jacobi, St. Petersburg. 
M. Khanikoff, St. Petersburg. 
Prof. A. Kolliker, Wurzburg. 
Prof. De Koninck, Liége. 
Professor Kreil, Vienna. 


Dr. A. Kupffer, St. Petersburg. 


| Dr. Lamont, Munich. 


Prof. F. Lanza. 

M. Le Verrier, Paris. 

Baron von Liebig, Munich. 

Professor Loomis, New York. 

Professor Gustav Magnus, Berlin. 

Professor Matteucci, Pisa. 

Professor von Middendorff, St. Petersburg. 

M. l’Abbé Moigno, Paris. 

Professor Nilsson, Sweden. 

Dr. N. Nordenskiold, Finland. 

M. E. Peligot, Paris. 

Prof. B. Pierce, Cambridge, U.S. 

Viscenza Pisani, Florence. 

Gustave Plaar, Stresburg. 

Chevalier Plana, Turin. 

Professor Pliicker, Bonn. 

M. Constant Prévost, Paris. 

M. Quetelet, Brussels. 

Prof. Retzius, Stockholm. 

Professor W. B. Rogers, Boston, U.S. 

Professor H. Rose, Berlin. 

Herman Schlagintweit, Berlin. 

Robert Schlagintweit, Berlin. 

M. Werner Siemens, Vienna. 

Dr. Siljestrom, Stockholm. 

M. Struvé, Pulkowa. 

Dr. Svanberg, Stockholm. 

M. Pierre Tchihatchef. 

Dr. Van der Hoeven, Leyden. 

Prof. E. Verdet, Paris. 

Baron Sartorius von Waltershausen, 
Gottingen. 

Professor Wartmann, Geneva. 


Report of the Council of the British Association, presented to the 
General Committee at Oxford, June 27, 1860. 


1. The Council were instructed by the General Committee at Aberdeen 
to maintain the establishment at Kew Observatory by aid of a grant of £500. 
They have received the following Report of the Committee to whom the 
working of the Observatory is entrusted. 


REPORT OF THE KEW COMMITTEE. XXX1 


_ 2. The continuance of Magnetic Observations, at stations indicated by the 
General Committee at the Leeds Meeting, has engaged the attention of H.R.H. 
the President, and of the Council; and they have had the advantage of co- 
operation on the part of the President and Council of the Royal Society. 
Every means has been adopted for pressing the subject on the favourable 
attention of the Government, but, it is to be regretted, hitherto without 
success. 

3. The importance of telegraphic communication between sea-ports of the 
British Isles, has been the subject of much attention since it was urged on 
the General Committee by the Aberdeen Meeting. The Council are happy 
to find that Admiral FitzRoy has been authorized to proceed in bringing to 
a practical issue the recommendations offered on this subject to the scientific 
department of the Board of Trade; and they. congratulate the Association 
on the share they have taken in a cause so dear to humanity. 

4. The expedition suggested by the Royal Geographical Society, and con- 
curred in by the General Committee of the British Association, is on its 
way; Capt. Speke, under the direction of the Admiralty, with his assistant, 
Capt. Grant, having sailed from Zanzibar. Sir R.1. Murchison, in reporting 
on this subject, expresses the obligation which is felt by the promoters of this 
great step for the exploration of Africa, to Lord John Russell, Secretary of 
State for Foreign Affairs. 

The Report of the Parliamentary Committee is received for presentation 
to the General Committee this day. 

5. At the Meeting this day, in pursuance of the Notice placed in the 
Minutes of the General Committee at Aberdeen, it will be proposed —“ That 
a permanent distinct Section of Anatomy and Physiology be established, in 
addition to that of Zoology and Botany.” 

The Council are informed that Invitations will be presented to the General 
Committee at its Meeting on Monday, July 2, to hold the next Meeting in 
Manchester; on behalf of the Literary and Philosophical Society of Man- 
chester, and other Institutions and Public Authorities of that city, from whom 
Invitations were received at previous Meetings. 

Invitations will also be presented to hold an early Meeting in Newcastle, 
on behalf of the Council and Borough of Newcastle-upon-Tyne, and to hold 
a Meeting in Birmingham in 1862, on behalf of the Birmingham and Midland 
Institute. 


Report of the Kew Committee of the British Association for the 
Advancement of Science for 1859-1860. 


Since the last Meeting of the British Association, the self-recording mag- 
netographs have been in constant operation under the able superintendence 
of Mr. Chambers, the magnetical assistant. 

A description of these instruments has been given by Mr. Stewart, the 
Superintendent, in a Report which is printed in the Transactions of the British 
Association for 1859. The drawings for the plates connected with this 
Report were made with much skill by Mr. Beckley, the mechanical assistant 
at Kew. 

It was mentioned in the last Report of this Committee, that a set of self- 
recording magnetic instruments, designed for the first of the Colonial Obser- 
vatories which have been proposed to Her Majesty’s Government, had been 
completed and set up in a wooden house near the Observatory. 

Shortly after the meeting at Aberdeen, the Chairman received a letter from 
Dr. P. A. Bergsma, Geographical Engineer for the Dutch possessions in the 


XXX1l REPORT—1860. 


Indian Archipelago, requesting that the Committee would assist him in pro- 
curing a set of self-recording magnetic differential instruments similar to 
those at Kew, the Dutch Government having resolved to erect such at their 
Observatory at Java. 

In consequence of this application, and as the instruments which had been 
completed were not immediately required for a British Observatory, it was 
resolved that they should be assigned to Dr. Bergsma; this gentleman has 
since arrived, and has for the last few weeks been engaged at the Observatory 
in the examination of his instruments. 

The usual monthly absolute determinations of the magnetic elements con- 
tinue to be made. 

Application having been made through Padre Secchi, of the Collegio Ro- 
mano, for a set of magnetic instruments, for both differential and absolute 
determinations, for the Jesuits’ College at Havanna, the whole to cost 600 
dollars, or about £150, General Sabine obtained, at a reasonable price, the 
three magnetometers that had formerly been employed at Sir T. Brisbane’s 
Observatory at Makerstoun, and also an altitude and azimuth instrument. 
With these instruments it is expected that the application from Havanna 
Observatory can be met within the sum named; the instruments are now in 
the hands of the workmen, and will be ready early in July. 

Two unifilars, supplied by the late Mr. Jones, for the Dutch Government 
(one for Dr. Bergsma, and the other for Dr. Buys Ballot), have had their 
constants determined. Observations have also been made with two 9-inch 
dip-circles belonging to General Sabine, which have been repaired by Barrow, 
and with two dip-circles and a Fox’s instrument designed for Dr. Bergsma. 

A set of magnetical instruments, consisting of a dip-circle, an azimuth 
compass, and a unifilar, previously used by Captain Blakiston, have been 
re-examined, and have been taken by Colonel Smythe, of the Royal Artillery, 
to the Feejee Islands. 

As it was feared that the Kew Standard Barometer might have been 
injured by the workmen who some time since were repairing the Observatory, 
a new one has been mounted. ‘The mechanical arrangements of this instru- 
ment have been completed in a very admirable manner by Mr. Beckley ; and 
the mean of all the observations made shows that the new Barometer reads 
precisely the same asthe old. This result is satisfactory, not only as showing 
that no change has taken place in the old Barometer, but as confirming the 
accuracy of the late Mr. Welsh’s process of constructing these instruments. 
The height of the cistern of the new Barometer above the level of the sea is 
33°74 feet. 

Mr. Valentine Magrath having quitted the Observatory, at his own request, 
on the 14tn of February last, Mr. George Whipple has taken his place as 
Meteorological Assistant, and has given much satisfaction. 

On the 12th of March, Thomas Baker was engaged at the weekly salary 
of 8s., to be raised to 10s. in six months if he gave satisfaction, which has 
hitherto been the case. 

Since the last meeting of the Association, 173 Barometers and 222 Ther- 
mometers have been verified at the Observatory. 

Professor Kupffer, Director of the Russian Magnetical and Meteorological 
Observatories, visited the Observatory, and was presented with a standard 
thermometer. 

Mr. J. C. Jackson, Lieutenant Goodall, R.E., and Mr. Francis Galton, 
F.R.S., have visited the Observatory, and received instructions in the mani- 
pulation of instruments. 

Mr. Galton has made some experiments at Kew Observatory, to determine 


. 


REPORT OF THE KEW COMMITTEE. XKXIil 


the most practicable method of examining sextants, and other instruments 
for geographical purposes. Considering that these instruments, after having 
been once adjusted, are liable to two distinct classes of error, the one constant 
for any given reading, and the other variable, it is an object to form Tables 
of Corrections for the constant errors of instruments sent for examination, 
and also to ascertain the amount of variable errors which might affect their 
readings. 

As a groundwork for examination, it is found that small mirrors may be 
permanently adjusted, at the distance of half a mile, so that when the rays 
of a mirror of moderate size, standing by the side of an assistant, are flashed 
upon them, they may re-reflect a brilliant star of solar light, towards the 
sextant under examination. 

By having four permanently fixed mirrors of this description, separated by 
intervals of 20°, 60°, and 40° respectively, and by flashing upon them with 
two looking-glasses of moderate size, it is possible, by using every combina- 
tion of these angles, to measure every twentieth degree, from 0° up to 120°. 

The disturbing effects of parallax are eliminated without difficulty, by 
mere attention to the way in which the sextant is laid on the table, or, in 
the case of a zero determination, by a simple calculation. 

Moreover, the brilliancy of the permanent mirrors is perfectly under con- 
trol, by the interposition of gauze shades in front of the looking-glasses that 
flash upon them. This renders an examination of the coloured shades a 
matter of great ease and certainty. 

Based upon these principles, Mr. Galton has drawn up a system for the 
thorough examination of sextants. Each would not occupy more than two 
hours in having its constant errors tabulated, and its variable errors deter- 
mined; nor would an outlay of more than £30 be required for the establish- 
ment of fixed tables and permanent marks. Difficulty is, however, felt in 
setting the system in action, owing to the absolute need of an assistant 
having leisure to undertake it. 

The sum of £179 12s. 6d. has been received from the Royal Society, 
to defray the expense of erecting a model house for the reception of the 
instruments for Colonial Magnetic Observatories. 

The Photoheliograph has been an occasional source of occupation to the 
mechanical assistant; but before daily records of the sun's disk can be ob- 
tained, it is absolutely requisite that an assistant should be appointed to aid 
Mr. Beckley, because his duties are of such a nature as to prevent his de- 
voting attention at fixed periods of the day to an object requiring so much 
preparation as is the case with photoheliography. Unfortunately, the funds 
at the disposal of the Committee are quite inadequate for this purpose; and 
unless a special grant be obtained, the Photoheliograph will remain very little 
used. 

At present Mr. Beckley is preparing the instrument, under Mr. De la Rue’s 
direction, for its intended trip to Spain, for the purpose of photographing the 
eclipse which takes place on July 18th. The expenses of these preparations, 
and of the assistants who will accompany Mr. De la Rue, will be defrayed 
out of the grant of the Royal Society for that object. 

The requisite preparations are somewhat extensive ; for it has been deemed 
necessary to construct a wooden observatory, and to make a new iron pillar 
to support the instrument, adapted to the latitude of the proposed station: 
both the observatory and iron pillar may be taken to pieces to facilitate their 
transport, 

The wooden house is 8 feet 6 inches square, and 7 feet high; it is entirely 
open at the top, except that portion divided off for a photographic room. 

1860. ¢ 


XXXiv REPORT—1860. 


The open roof will be covered by canvas when the observatory is not in use ; 
and when in use, the canvas will be drawn back, so as to form an outer casing 
at some little distance from the wall of the photographic room; and, in order 
to keep this room as cool as possible, the canvas will, in case of need, be kept 
wetted. 

The chemicals and chemical apparatus will be packed in duplicate sets, so 
as to provide as far as possible against the contingency of loss, by breakage 
or otherwise, of a part of them. 

Mr. Downes, of the firm of Cundall and Downes of Bond Street, has 
promised to accompany the expedition; Mr. Beckley will also go; and Mr. 
De la Rue has engaged Mr. Reynolds to assist in the erection of the observa- 
tory in Spain, and in the subsequent photographic operations. 

The Admiralty, on the representation of the Astronomer Royal, have pro- 
vided a steam-ship to convey this and other astronomical expeditions to Bil- 
bao and Santander. It is proposed that the Kew party should land at Bilbao 
and proceed to Miranda. Mr. Vignoles, who is constructing the Tudela and 
Bilbao railway, has kindly promised his aid and that of his staff of assist- 
ants, to promote the objects of the expedition, and promises, on behalf of the 
contractors, the use of horses and carts for the conveyance of the apparatus. 
The expedition will sail from Portsmouth on the 7th of July; and, should the 
weather prove favourable, there is reasonable hope that the various phases 
of the eclipse will be successfully photographed. Whether the light of the 
corona and red prominences will be sufficiently bright to impress their images, 
when magnified to four inches in diameter, is a problem to be solved only by 
direct experiment. 

Professor William Thomson (of Glasgow) having expressed a desire that 
the practical utility of his self-recording electrometer should be tried at Kew, 
his wish has been acceded to and the instrument received, and it is expected 
that it will shortly be in operation under his direction. 

A Report has been completed by the Superintendent on the results of the 
Magnetic Survey of Scotland and the adjacent islands in the years 1857 and 
1858, undertaken by the late Mr. Welsh. This Report is printed in the 
Transactions of the British Association for 1859. 

The following correspondence has taken place between General Sabine 
and the Rev. William Scott, Director of the Sydney Observatory :— 


“ Observatory, Sydney, March 2, 1860. 


“ Srr,—The great interest which you take in the promotion of Magnetical 
Science encourages me to address you on the subject of the establishment of 
a Magnetical Observatory at Sydney. The report which I send you by this 
mail will explain to you the character and position of the Astronomical Ob- 
servatory under my direction. 

“JT am convinced that an application to our Government, from influential 
persons at home, for the establishment of magnetical observations on not 
too expensive a scale, would be readily attended to. Iam not practically 
acquainted with any magnetical observatory, with the exception of that at 
Greenwich, and am ignorant of the cost of a set of instruments, and the 
exact amount of space required for working them; but I believe we could 
find sufficient room in the observatory without any additional building; they 
would be under my own supervision, and all that would be required would 
be an additional assistant, to share with myself and my one assistant in 
observing and computing. The Governor-General, Sir W. Denison, would, 
though powerless as regards public money, exert his influence in favour of 
such an object. 


REPORT OF THE KEW COMMITTEE. XXXV 


“ Trusting that you will take the matter into consideration, and excuse the 
liberty I have taken in addressing you, 
“Tam, Sir, 
‘* Your obedient Servant, 
(Signed) “W. Scort, 
« Astronomer for N. S. Wales.” 
“ Major-General Sabine.” 


“13 Ashley Place, London, May 8, 1860. 
y y 


« Str,—I lose no time in replying to your letter of March 2, received this 
day. ‘The self-recording magnetical instruments at Kew have been in action 
nearly two and a half years—a sufficient time to test their merits or defects. 
I have myself completed the analysis and reduction of the first two years (1858 
and 1859) of the Observations of the Declinometer, and can therefore speak of 
my own knowledge of their performance, as far as that element is concerned. 
The Photographic Traces, recording both the zero line and the actual move- 
ments of the magnet, can be measured with tolerable confidence to the third 
place of decimals of an inch, the inch in the Kew instrument being equiva- 
lent to 22 minutes of arc. The reading is consequently made to the 1000th 
part of 22 minutes of declination. The record is of course continuous; but, 
for the purpose of computing the results, howrly readings have been tabulated. 
In the first year the trace failed in 107 out of 8760 hours, chiefly from 
failure in the supply of gas, which is brought by pipes from Richmond, a 
considerable distance off. This inconvenience has been remedied by the 
construction at the Observatory itself, at a small expense, of a water regu- 
lator, through which the supply from Richmond passes, and there is now no 
reason why the trace should ever fail. I have now in course of analysis and 
reduction the same years of the observations of the horizontal and vertical 
force magnetographs, and have no reason hitherto to believe tnat the record 
of those two elements will be inferior to that of the declination. The three 
instruments, with the clock which keeps the registering papers in revolution, 
together with reading telescopes placed for eye observation, either to accom- 
pany or to be independent of self-registry, occupy an interior space of about 
16 feet by 12, including a passage round for the observer. The cost of such 
a set of instruments, complete in every respect, is £250; and four months 
must be allowed for making them from the date of the order, as well as an 
additional month for their careful verification at Kew (should that be de- 
sired), where a detached building has been erected for this particular pur- 
pose, in which they may be kept in work in comparison with the Kew instru- 
ments. A detailed description of these instruments is now in the press, and 
will be published in June in the volume of Reports of the British Association. 
The results of the first two years of the Declinometer observations, showing 
what are deemed at present to be the most useful modes of eliciting the re- 
sults, will be printed in the ‘ Proceedings of the Royal Society’ in the present 
summer, and the first two years of the horizontal and vertical force magneto- 
graphs in the same publication later in the year. A small adjoining room is 
requisite, opening if possible into the instrument-room, which should contain 
suitable troughs for the preparation of the paper to receive the traces, and 
to fix them. It is important to diminish as much as possible the changes of 
temperature in the Observatory itself, exclusive of the effect of the instrument 
cases, which have adaptations for that purpose. So far in regard to differential 
instruments. For absolute determinations and secular changes a small de- 
tached house is required, say 12 feet by 8, in which equality of temperature 
need not be regarded, but which must be at a sufficient distance from other 

e2 


Xxxvi REPORT—1860. 


buildings containing iron, and have copper fittings. The instruments required 
for these purposes are an inclinometer and a unifilar, the latter having pro- 
vision for the experiments of deflection and vibration, as well as for the abso- 
lute declination: the cost of the first is £30, and of the second £45; both may 
be verified, if desired, at Kew. The little work which is sent to you by the 
same post as this letter contains a full description of these instruments, and 
directions for their use. In addition to the charges named above, making in 
all £325, the cost of packing, freight, and insurance will have to be taken 
into the account. 

“ One assistant will suffice, as you suggest, for keeping the magnetometers 
in action, and for tabulation. The absolute values, and the calculation of the 
results of all the instruments, would be, I presume, the work of the Director 
of the Observatory himself. Provision must also be made for a supply of 
chemicals, stationery, and gas. Should it be thought desirable that the instru- 
ments should be prepared and verified under the superintendence of the Com- 
mittee of the Kew Observatory, a request to that effect, transmitted by your- 
self through the Governor of the Colony to the Chairman of the Committee 
of the Kew Observatory, Richmond Park, London, $.W., would, I am sure, 
meet immediate attention. That such an institution at the head-quarters of 
our Australian dominions would be as honourable to those who should be 
instrumental in its establishment as it would be beneficial to magnetical 
science, must be a matter of general recognition, and it would, I am per- 
suaded, find a warm supporter in your present most excellent Governor. 

‘TI remain, Sir, 
“ Your obedient Servant, 
(Signed) “ EDWARD SABINE.” 
“ The Rev. W. Scott.” 


From the following correspondence which has taken place between Her 
Majesty’s Government and the President of the Royal Society, it will be 
seen that the establishment of a Magnetical Observatory at Vancouver 
Island is postponed, in consequence of the war with China precluding the 
establishment at present of a corresponding observatory at Pekin :— 


“Treasury Chambers, 16th May, 1860. 

“ Srr,—I am directed by the Lords Commissioners of Her Majesty’s 
Treasury to acquaint you that My Lords have had under their further con- 
sideration the establishment of an Observatory at Vancouver Island, and 
the insertion in the Estimates of this year of a vote for that service. 

“ My Lords are fully sensible of the importance of obtaining a series of 
accurate Magnetical Observations at the stations recommended by the Council 
of the British Association, and it would give them great pleasure to assist 
without further delay in forwarding objects so interesting for the cause of 
science. 

“The numerous and pressing claims, however, on the public finances in 
the present year make it imperative upon My Lords to submit no fresh esti- 
mate to Parliament which is not of a very urgent character, and where the 
total limit of expense to be incurred has not been accurately ascertained. 

“In the present instance My Lords must observe that you appear to be 
under some misapprehension in supposing that any engagement was entered 
into by the late Government to establish a Magnetic Observatory at Pekin or 
elsewhere. On the contrary, the letter of this Board of 6th December, 1858, 
to Lord Wrottesley states that, ‘whatever may be the public advantages to 
be derived from the proposed new establishments, the object would not, 


REPORT OF THE KEW COMMITTEE. XXXVI 


it appears, be sacrificed by postponement, and, looking to tae extent of 
the other claims upon the public finances already existing, My Lords 
have thought it right to defer the consideration of the question until next 
year.’ 

we The letter then further states, that the three Magnetical Observatories 
at the Cape of Good Hope, St. Helena, and Toronto, which were originally 
sanctioned in an estimate of about £3000 for three years, had in fact cost 
£11,000 for that period, and, in all, had put the country to an expense of 
nearly £50,000. ‘This considcration alone suffices to show the necessity for 
very careful investigation by the Government before any step is taken which 
might commit the country to further expense. The circumstances referred 
to in the letter in question continue in full foree; and an important further 
argument against undertaking the proposed Observatory at Vancouver 
Island at the present moment is furnished by the political events which have 
since occurred in China. In General Sabine’s able letter of the Ist January, 
1859, it is stated that, ‘without entering into the comparative scientific value 
of Vancouver Island and Pekin as magnetic stations,—both being highly 
important,—this much is certain, that, whatever might be the value of either, 
that value would be greatly enhanced—far more than doubled—by there 
being a simultaneous and continuous record at both stations; and Sir John 
Herschel remarks that the importance of a five years’ series of observations 
at one of the proposed stations without the others would be grievously dimi- 
nished, and the general scope of the project defeated.’ 

“ As the present state of things in China precludes the establishment of a 
Magnetic Observatory at Pekin, or any point in the Chinese Empire suffi- 
ciently to the north to correspond with a station at Vancouver Island 
(though there is reason to hope that this state of things may be of short 
duration ), it would appear desirable even in the interests of science to postpone 
the consideration until something more certain can be ascertained as to the 
possibility of meeting what Sir John Herschel and General Sabine consider 
such an essential requisite, viz. the commencement and continuance of simul- 
taneous observations at Vancouver Island and at a point in China nearly in the 
same parallel of latitude. The interval which must elapse until the political 
state of affairs in China may render such an establishment possible may be 
usefully employed in obtaining the most accurate estimate possible of the 
actual cost of founding and maintaining each station for the period requisite 
for the complete attainment of the scientific objects in view, so as to enable 
Her Majesty’s Government, when the proper time shall arrive, if they shall 
decide on doing so, to submit a vote to Parliament with confidence as to the 
amount of expense which they may ask the nation to defray in the interests 
of science. 

‘Cl ain, Sin 
“ Your obedient Servant, 
(Signed) “ Gro. A. HAMILTON.” 


“ The President of the Royal Society.” 


“May 23rd, 1860. 
“My pear Sir,—In Mr. Hamilton's letter (returned herewith) he has 
referred to Sir Charles Trevelyan’s communication to Lord Wrottesley of the 
6th December, 1858, expressing the desire of the Lords Commissioners of 
the Treasury to postpone to the following year the consideration of the esta- 
blishment of the Colonial Magnetic Observatories which had been recom- 
mended by the Royal Society and the British Association for the Advance- 


XXXVili REPORT—1860. 


ment of Science ; but Mr. Hamilton has omitted altogether to refer to the 
interview which took place between the President of the British Association 
and Sir Charles Trevelyan subsequent to that communication, viz. on the 
18th of December, 1858, when Sir Charles Trevelyan stated that ‘if asingle 
station for magnetical and meteorological observations were applied for [in- 
timating Pekin as its locality] by the Joint Committee of the Royal Society 
and the British Association, My Lords would be disposed to comply with 
such application. (See Report of the Council of the British Association, 
September 1859.) 

“ Political events which became known shortly after that interview made 
it manifestly unadvisable to apply for a station in China; but the scientific 
importance of procuring systematic magnetical researches at other stations 
which had been named in the original application from two Societies, in parts 
of the globe which were conveniently accessible and under British dominion, 
remained as before. In these respects Vancouver Island was unobjectionable, 
and was therefore substituted for ‘a station in China’ in the application, 
which, consistently with Sir Charles Trevelyan’s communication of the 18th 
December, 1858, was made by the Joint Committee of the two Societies. The 
confident expectations thus founded being known in the United States by 
the publications of the Reports of the Joint Committee of the Royal Society 
and British Association, the Government of the United States authorized the 
establishment of Magnetical Observatories at a station on the east side of the 
United States, and at another on the south coast, both designed to cooperate 
with the British Observatory to be established on Vancouver Island ; the three 
stations being obviously remarkably well selected for systematic researches 
over that large portion of the globe. The two observatories of the United 
States’ Government have been established, and commenced their work at 
the beginning of the present year. 

“In reference to the aggregate amount of expenditure incurred by the 
magnetical researches recommended to Government by the Royal Society 
and British Association in the last twenty years, it may be remarked that, the 
researches being altogether of a novel character, the continuance of the 
Observatories, when first asked for in 1839, was for a very limited period. 
It was, in fact, an experiment, and their longer continuance would not have 
been recommended had not the experiment proved eminently successful, and 
such as to justify the prosecution of the researches. The subject was there- 
fore brought afresh under the consideration of Government in 1845 and again 
in 1849, and the further expenditure to be incurred received the sanction of 
the Treasury on both occasions, as have also, on other occasions, the magnetie 
surveys connected with the Observatories. It is possible that the aggregate 
amount of expenditure thus sanctioned and incurred may not be overstated 
at £50,000. It is an average amount not exceeding £2500 a year for this 
great branch of physical science. 

‘“‘T am not myself the proper authority to say whether the gain to science, 
and to the estimation in scientific respects in which this country is held by 
other nations, be, or be not, an equivalent for this expenditure; but I may be 
permitted to refer to the opinion expressed by the Joint Committee of the 
two Societies, consisting, as is well known, of persons holding high places in 
public estimation for their general knowledge and good judgment, as well 
as possessing the highest scientific eminence :—‘ Your Committee, looking at 
this long catalogue of distinct and positive conclusions already obtained, feel 
themselves fully borne out in considering that the operation, in a scientific 
point of view, has proved, so far, eminently remunerative and successful, and 
that its results have fully equalled in importance and value, as real accessions 


REPORT OF THE KEW COMMITTEE. XXXIX 


to our knowledge, any anticipations which could reasonably have been formed 
at the commencement of the inquiry.’ 
“ Believe me, my dear Sir, 
“ Faithfully yours, 
(Signed) “ EDWARD SABINE.” 


“ Sir B. C. Brodie, Bart., P.R.S.” 


Mr. Hamilton to the President of the Royal Society, in reply to his letter of 
Qnd June (not given here). 


“Treasury Chambers, June 14, 1860. 

“ Sir,—In reply to your letter of the 2nd inst., with its enclosure from 
General Sabine relative to the establishment of Colonial Magnetic Observa- 
tories, I am directed by the Lords Commissioners of Her Majesty’s Treasury 
to state that, without entering into the question what verbal assurances may 
have been given in December 1858 by the then Assistant Secretary, Sir Charles 
Trevelyan, of which no record was made, their Lordships observe that the 
main ground of their letter of the 16th May, 1860, remains unaffected, viz. 
that, in the opinion of the highest scientific authorities, whatever might be 
the value of observations at Vancouver Island, that value would be greatly 
increased by simultaneous observations at some station in the North of China, 
and, on the other hand, would be ‘ grievously diminished’ if no station in 
China was established. Under these circumstances, their Lordships thought 
it desirable to postpone for a short time the consideration of the question, in 
the hope that it might be considered under a different state of things in China, 
rendering possible the attainment of the greatest amount of scientific advan- 
tage from the expenditure of public money, in case that expenditure should 
be decided upon. 


“Tam, Sir, 
“ Your obedient Servant, 
(Signed) “G. A. HamILToN.” 


General Sabine has written the following letter to Dr. Bache, who had 
intimated to him that, in the event of Her Majesty’s Government declining to 
establish a magnetical observatory at Vancouver Island, it was the wish of 
the United States’ Government to establish one in Washington Territory, in 
the vicinity of Vancouver Island :— 


“May 22, 1860, 


“Dear Bacue,—I waited to reply to yours of April 13th until we should 
have received the reply of our Government regarding the Vancouver Island 
Observatory. Mr. Gladstone has availed himself of some expressions in 
Sir John Herschel’s letters and mine (to the effect of the far greater import- 
ance of having observations on the Chinese as well as on the American side 
of the Pacific to having either separately) to postpone a decision regarding 
Vancouver Island until our relations with China shall enable our Govern- 
ment to consider the question of establishing both simultaneously. Our pro- 
position, therefore, has fallen to the ground, and it is quite open to your 
Government to occupy the field which you were willing to concede to us in 
consideration of the forward part which our Government has hitherto taken 
in magnetic researches. 

“Now in regard to the instruments, which, as you are probably aware, 
have been prepared at my own risk, in order that, should our Government 
accede to the recommendation made by the Royal Society and British Asso- 


xl REPORT—1860. 


ciation, the time might be saved which must otherwise have been lost in their 
preparation. They have been made on the model of those which have been 
in use at the Kew Observatory since January 1858. An account of these isin 
the press, and will be published in the volume of Reports of the British Asso- 
ciation for 1859-1860, which must be in circulation next month. I have 
thoroughly examined and computed the declination results for 1858 and 1859, 
by means of tabulated hourly values, and am now engaged in the same cal- 
culation of the Bifilar and Vertical Force Magnetometers. The Declination 
Report will be presented to the Royal Society, and printed in the ‘ Proceed- 
ings’ in the course of the summer, as well as the results of the Force Mag- 
netometers for the same two years, as soon as I am able to draw up the report 
in due form and order. But Iam able tosay, regarding all the three elements, 
that the instruments are eminently successful. Independent of the continucty 
of the record (which is of course a great thing in itself), the hourly tabula- 
tions are far more consistent and satisfactory than were the eye-observations 
at any of our observatories. 

“In preparing a second set of instruments, therefore (which we have done 
for the proposed Netherlands Observatory in Java), we have had very few 
improvements to introduce, except the addition of reading-telescopes for each 
instrument—so that we may always retain the power of eye-observation, 
either in addition to or substitution for photographic records. Dr. Bergsma, 
the Director of the Java Observatory, is now at Kew, observing with his in- 
struments, in comparison with those in our own Observatory (as we have a 
separate building for the instruments on trial), and will take them away 
towards the end of June. ‘These of course will be paid for by the Netherlands 
Government, having been ordered expressly for them. There will then be the 
third set, which have been prepared for Vancouver, and which are ready to 
succeed the Java instruments in the experimental house. A few very trifling 
improvements have been introduced in these—none worthy of being noticed 
here. They at present stand as mine, and I shall be indebted £250 for them. 
The decision of Government, as communicated to the President of the Royal 
Society, makes no reference to my responsibility on their account. I am, 
therefore, to say the least, quite free to dispose of them as I may please. 
Now I am not rich enough to offer them as a Joan to your ‘ Washington 
Territory ’ Observatory ; but if you desire to have differential determinations 
there in addition to absolute determinations, I am persuaded that you could 
not have better instruments than these would be; and I consider myself as 
quite free to offer you the refusal of them, asking only in return that you 
will give me as early a reply as may be convenient, because I have some 
reason to expect that I may receive an application from the Sydney Obser- 
vatory to obtain a duplicate of the Kew instruments; in which case, if you 
had not claimed them in the meantinie, I should direct these to be sent to 
Sydney. -- Sincerely yours, 

(Signed) “ EDWARD SABINE.” 


“ Dr. Bache, F.R.S., Director of the 
Coast Survey of the United States.” 


The reply to this letter has not yet been received; but in the meantime 
the following application has come for a set of magnetical instruments for 
absolute determinations from Dr. Smallwood, Professor of Meteorology at 
M°Gill College in Montreal, Canada:— 

“St. Martin, Isle Jésus, May 2], 1860. 


- © Srr,—I duly received yours of the 16th of July last, in reference to the 


REPORT OF THE KEW COMMITTEE. xli 


establishment of a Magnetic Observatory here, in connexion with observa- 
tions on meteorology and atmospheric electricity, and deferred writing until 
I was in a position to acquire the instruments necessary. 

* You said in your communication that ‘£80 or thereabouts was required;’ 
and you were kind enough to add, with a spirit of generosity I could not 
expect, ‘that every care should be taken to superintend the construction of 
such instruments, to verify them, and to determine their constants, and have 
them carefully packed and sent out.’ 

“ The object of the present letter is to ascertain, Ist, the exact cost (if pos- 
sible); 2nd, to whom the amount shall be forwarded; Srd, when the instru- 
ments would probably be ready ; 4th, a short list of what are to be sent. 

“JT feel that Iam asking too much from you; but a knowledge of your 
devotion to a science which you have so much extended, makes me feel less 
diffident, and I have thrown myself upon your kindness. 

“T have also to acknowledge the receipt of a Book of Instructions, &c., 
with thanks. 

“ So soon as I get a reply from you, I will at once transmit the amount 
with the order, and submit a plan of the building. 

* Believe me to remain, with great consideration and respect, 
“ Yours faithfully, 
(Signed) “ C, SMALLWoop.” 
* General Sabine, London.” 


Instruments to meet this request are in preparation. 


The Committee have thought that it might not prove uninteresting to the 
members of the British Association, if, in this Report, a short description 
were given of the Kew Observatory, and of the nature and amount of work 
which is accomplished therein. 

The Observatory is situated in the middle of the old Deer-park, Richmond, 
Surrey, and is about three-quarters of a mile from the Richmond Railway 
Station. Its longitude is 0° 18! 47" W., and its latitude is 51°28’ 6" N. It 
is built north and south. The repose produced by its complete isolation is 
eminently favourabie to scientific research. In one of the lower rooms a set 
of self-recording magnetographs, described in the Report of the last meeting 
of this Association, is constantly at work. ‘These instruments, by the aid of 
photography, furnish a continuous record of the changes which take place in 
the three magnetic elements, viz. the declination, the horizontal force, and the 
vertical force. The light used is that of gas, in order to obtain which, pipes 
have been carried across the Park to the Observatory, at an expense of £250, 
which sum was generously defrayed by a grant from the Royal Society. 

Attached to this room is another, of a smaller size, in which the necessary 
photographic operations connected with magnetography are conducted. 

In the story above the basement, the room by which the visitor enters the 

Observatory is filled with apparatus. Much of this is the property of the 
Royal Society, and some of the instruments possess a historical value; for 
instance, the air-pump used by Boyle; and the convertible pendulum designed 
by Captain Kater, and employed by him, and subsequently by General Sabine, 
in determining the length of the pendulum vibrating seconds. 
_ An inner room, which opens from this one, is used as a library and sitting- 
room, and in it the calculations connected with the work of the Observatory 
are performed. In this room dipping-needles and magnets, which it is neces- 
sary to preserve from rust, are stored. Here also the MS. of the British 
Association Catalogue of Stars is preserved. 

A room to the east of this contains the standard barometers, and the appa- 


xlii REPORT—1860. 


ratus (described by Mr. Welsh in the ‘ Transactions’ of the Royal Society, 
vol. 146. p. 507) for verifying and comparing marine barometers with the 
standard. This room has also accommodation for the marine barometers 
sent for verification. In the middle of the room is a solid block of masonry, 
extending through the floor to the ground below. To this an astronomical 
quadrant was formerly attached ; it is now used as a support for the standard 
barometers. This room contains also a Photographic Barograph invented 
by Mr. Francis Ronalds, which, though not at present in operation, may 
serve as a model for any one who wishes to have an instrument of this 
description. It is described by Mr. Ronalds in the Report of the British 
Association for 1851. 

In a room to the west of the Library, thermometers for the Board of Trade, 
the Admiralty, and opticians, are compared with a standard thermometer by 
means of a very simple apparatus devised by the late Mr. Welsh. 

The Observatory also possesses a dividing-engine by Perreaux, by means of 
which standard thermometers are graduated. It was purchased by a grant 
from the Royal Society. 

In this room the pure water required for photographic processes is obtained 
by distillation; and here also a small transit telescope is placed for ascertain- 
ing time. The transit instrument is erected in a line between two meridian 
marks—one to the north and the other to the south of the Observatory ; so 
that, by means of suitable openings, either of these marks may be viewed by 
the telescope. 

In a higher story is the workshop, containing, among other things, a slide- 
lathe by Whitworth, and a planing machine by Armstead, both of which were 
presented to the Kew Observatory by the Royal Society. 

In the dome is placed the Photoheliograph for obtaining pictures of the 
sun’s disk; attached to the dome there is a small chamber in which the 
photographic processes connected with the photoheliograph are conducted. 
This chambe 1's supplied with water by means of a force-pump. A self= 
recording Robinsons anemometer jsalso attached to the dome. 

In addition to the rooms now specified, there are the private apartments 
attached to the Observatory. 

On the north side of the Observatory there is an apparatus similar to that 
used at the Toronto Observatory for containing the wet- and dry-bulb, the 
maximum and the minimum thermometers. 

The model magnetic house, elsewhere alluded to in this Report, stands at a 
distance of about 60 yards from the Observatory ; and the small wooden 
house in which the absolute magnetic observations are made, at a distance 
of about 110 yards. These houses are within a wooden paling, which fences 
them off from the remainder of the Park, and encloses about one acre of 
ground attached to the Observatory. 

The work done may now be briefly specified. In the first place, the self- 
recording magnetographs, as already mentioned, are kept in constant opera- 
tion, and record the changes continually occurring in the magnetic elements. 

The photographs are sent to General Sabine’s establishment at Woolwich, 
to undergo the processes of measurement and tabulation. 

In the model magnetic house there is at present a set of magnetographs 
which Dr, Bergsma will take to Java. When this set is removed another will 
supply its place, in readiness for any other Observatory, colonial or foreign, 
at which it may be required. 

In the house for absolute determinations, monthly values of the declination, 
dip, and horizontal magnetic force are taken, and magnetic instruments for 
foreign or colonial observatories have their constants determined, 


xiii 


REPORT OF THE KEW COMMITTEE. 


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xliv REPORT—1860. 


In the meteorological department, all the barometers, thermometers, and 
hydrometers required by the Board of Trade and the Admiralty have their 
corrections determined; besides which, similar instruments are verified for 
opticians. Standard thermometers also are graduated, and daily meteoro- 
logical observations are made, an abstract of which is published in the 
‘ Illustrated London News.’ 

Instruction is also given in the use of instruments to officers in the army 
or navy, or other scientific men who obtain permission from the Committee. 

All this amount of work, it is believed, can be executed by the present 
staff, consisting of the superintendent, three assistants (magnetical, mecha- 
nical, and meteorological), and a boy; but the expense attending it is greater 
than the present income of the Observatory, furnished by the British Asso- 
ciation, will support. 

In the resolution of the British Association of the 14th September, 1859, 
it was recommended to Government, at the instance of the joint committee of 
the Royal Society and British Association, that the sum of £350 per annum 
should be placed at the disposal of the general superintendent of the mag- 
netical observations ; this sum was intended to have defrayed the expenses 
attending the magnetical department of the Observatory and the observa- 
tions of the sun’s spots. It will be seen, however, from the correspondence 
contained in an earlier part of this Report, that this source of income is not 
yet available. 

Joun P. GAsstotT, 

June 18, 1860. Chairman. 


Report of the Parliamentary Committee to the Meeting of the British 
Association at Oxford in June 1860. 


The Parliamentary Committee have the honour to report as follows :— 

No subject of sufficient importance to require any especial notice has occu- 
pied their attention during the past year, nor indeed was there any matter 
referred to them at the last Meeting of the Association. 

There are now either two or three vacancies in that portion of the Com- 
mittee which represents the House of Commons, according as it shall be de- 
termined whether the vacancy caused in that Section by Lord de Grey’s 
taking his seat in the House of Lords is or is not to be filled up, 


WrottTeEsLey, Chairman. 
May 28, 1860. 


RECOMMENDATIONS OF THE GENERAL COMMITTEE. xly 


RECOMMENDATIONS ADOPTED BY THE GENERAL COMMITTEE AT THE 
Oxrorp MEETING IN JUNE AND JULY 1860. 


[When Committees are appointed, the Member first named is regarded as the Secretary of 
the Committee, except there be a specific nomination. ] 


Involving Grants of Money. 


That the sum of £500 be appropriated to the maintenance of the Esta- 
blishment in Kew Observatory, under the direction of the Council. 

That a sum not exceeding £90 be granted for one year for the payment 
of an additional Photographer for carrying on the Photo-heliographic Ob- 
servations at Kew. 

That a sum not exceeding £30 be placed at the disposal of Mr. Broun, 
Dr. Lloyd, and Mr. Stone, for the construction of an Induction Dip Circle, 
in connexion with the Observatory at Kew. 

That a sum not exceeding £10 be placed at the disposal of Professor 
Tyndall and Mr. Ball, for providing Instruments fur making Observations in 
the Alps, and for printing the formule for the use of travellers. 

That the Balloon Ascent Committee, consisting of Prof. Walker, Prof, 
W. Thomson, Sir D. Brewster, Dr. Sharpey, Dr. Lloyd, Col. Sykes, General 
Sabine, and Prof. J. Forbes, be reappointed, with the addition of Mr. Broun ; 
and that the sum of £200 be placed at their disposal for the purpose. 

That Dr. Matthiessen be requested to prosecute his Experiments on the 
Chemical Nature of Alloys; and that the sum of £20 be placed at his dis- 
posal for the purpose. 

That Prof. Sullivan be requested to continue his Experiments on the Solu- 
bility of Salts at Temperatures above 100° Cent., and on the mutual Action 
of Salts in Solution ; and that the sum of £20 be placed at his disposal for 
the purpose. 

That Prof. Voelcker be requested to continue his investigation on Field 
Experiments and Laboratory Researches on the Constituents of Manures 
essential to Cultivated Crops; and that the sum of £25 be placed at his 
disposal for the purpose. 

That Mr. Alphonse Gages be requested to continue his Experiments on the 
Mechanico-Chemical Analysis of Minerals; and that the sum of £20 be 
placed at his disposal for the purpose. 

That Mr. Mallet be requested to carry on his Experiments on Earthquake 
Waves ; and that the sum of £25 be placed at his disposal for the purpose. 

That additional excavations be made at Dura Den by the Committee, now 
consisting of Dr. Anderson, Prof. Ramsay, Prof. Nicol, and Mr. Page; that 
Mr. J. B. Jukes be added to the Committee; and that the sum of £20 be 
placed at their disposal for the purpose. 

That Mr. J. Gwyu Jeffreys, Dr. Lukis, Mr. Spence Bate, Mr. A. Hancock, 
and Dr. Verloren be a Committee for the purpose of Reporting on the best 
mode of preventing the ravages of the different kinds of Teredo and other 
Animals in our Ships and Harbours; that Mr. J. Gwyn Jeffreys be the 
Secretary ; and that the sum of £10 be placed at their disposal for the purpose. 

That Mr. Sclater, Dr. A. Giinther, and Mr. R. T. Tomes be a Committee 
for the purpose of preparing and printing a Report on the Present State of 
our Knowledge of the Terrestrial Vertebrata of the West India Islands ; 
that Mr. Sclater be the Secretary ; and that the sum of £10 be placed at 
their disposal for the purpose. 

That Mr. Robert MacAndrew and the following gentlemen be a Com- 


xlvi REPORT—1860. 


mittee for General Dredging purposes :—Mr. R. MacAndrew, Chairman; 
Mr. G. C. Hyndman, Dr. Edwards, Dr. Dickie, Mr. C. L. Stewart, Dr. Colling- 
wood, Dr. Kinahan, Mr. J. S. Worthey, Mr. J. Gwyn Jeffreys, Dr. E. Perceval 
Wright, Mr. Lucas Barrett, and Professor J. R. Greene. That Mr. Robert 
MacAndrew be the Secretary ; and that the sum of £25 be placed at their 
disposal for the purpose. 

That Dr. Ogilvie, Dr. Dickie, Dr. Dyce, Prof. Nicol, and Mr. C. W. Peach 
be a Committee for the purpose of Dredging the North and East Coasts 
of Scotland. That Dr. Ogilvie be the Secretary ; and that the sum of £25 
be placed at their disposal for the purpose. 

That the surviving members of the Committee appointed in the year 1842, 
viz. Mr. C. Darwin, Rev. Professor Henslow, Rev. L. Jenyns, Mr. W. Ogilby, 
Professor Phillips, Sir John Richardson, Mr. J. O. Westwood, Professor Owen, 
Mr. W. E. Shuckard, and Mr. G. R. Waterhouse, for the purpose of pre- 
paring Rules for the establishment of a Uniform Zoological Nomenclature, be 
reappointed, with the addition of Sir William Jardine, Bart., and Mr. P. L. 
Sclater. That Sir W. Jardine be the Secretary ; and that the sum of £10 be 
placed at their disposal for the purpose of revising and reprinting the Rules. 

That Mr. Sclater and Dr. F. Hechstetter be a Committee for the purpose 
of drawing up a Report on the Present State of our Knowledge of the Species 
of Apteryz living in New Zealand. That Mr. Sclater be the Secretary ; and 
that the sum of £50 be placed at their disposal for the purpose. 

That Dr. Collingwood be requested to dredge in the Estuaries of tne 
Mersey and Dee ; and that the sum of £5 be placed at his disposal for the 
purpose. 

That Dr. Edward Smith, F.R.S., and Mr. Milner be a Committee for the 
purpose of prosecuting inquiries as to the effect of Prison Diet and Discipline 
upon the Bodily Functions of Prisoners. That Dr. Edward Smith be the 
Secretary; and that the sum of £20 be placed at their disposal for the 
purpose. 

That Mr. T. Wright, Mr. J. B. Davis, and Mr. A. G. Hindlay be a Com- 
mittee for the purpose of exploring entirely the piece of ground at Uriconium 
in which the human remains have been found, in order to examine more 
fully the circumstances connected with the discovery, and to obtain the 
similar Skulls which may still remain under ground. ‘That Mr. T. Wright 
be the Secretary ; and that the sum of £20 be placed at their disposal for the 
purpose. 

That Professor James Thomson (of Belfast) be requested to continue his 
Experiments on the Gauging of Water; and that the sum of £10 be placed 
at his disposal for the purpose. 

That the Committee on Steam-ship Performance be reappointed, to report 
proceedings to the next Meeting ; that the attention of the Committee be 
also directed to the obtaining of information respecting the performance of 
vessels under Sail, with a view to comparing the results of the two powers 
of Wind and Steam, in order to their most effective and economical combi- 
nation ; and that the sum of £150 be placed at their disposal for this purpose. 
The following gentlemen were nominated to serve on the Committee :— 
Vice-Admiral Moorsom; The Marquis of Stafford, M.P.; The Earl of Caith- 
ness; The Lord Dufferin; Mr. William Fairbairn, F.R.S.; Mr.J. Scott Russell, 
F.R.S.; Admiral Paris, C.B.; The Hon. Captain Egerton, R.N.; Mr. William 
Smith, C.E.; Mr. J. E. M¢Connell, C.E.; Prof. Rankine, LL.D.; Mr. J. R. 
Napier, C.E.; Mr. R.Roberts,C.E.; Mr. Henry Wright, Honorary Secretary ; 
with power to add to their number. 

That Prof. Phillips be requested to complete and print, before the Man- 


RECOMMENDATIONS OF THE GENERAL COMMITTEE.  xlvii 


chester Meeting, a Classified Index to the Transactions of the Association 
from 1831 to 1860 inclusive; that he be authorized to employ, during this 
period, an Assistant; and that the sum of £100 be placed at his disposal for 
the purpose. 


Applications for Reports and Researches. 


That Mr. H. J. S. Smith be requested to continue his Report on the 
Theory of Numbers. 

That Mr. Cayley be requested to draw up a Report on certain Problems 
in Higher Dynamics. 

That Mr. B. Stewart be requested to draw up a Report on Prevost’s 
Theory of Exchanges, and its recent extensions. 

That Prof. Stokes be requested to draw up a Report on the Present State 
and Recent Progress of Physical Optics. 

That Dr. Dickie be requested to draw up a Report on the Flora of Ulster, 
for the next Meeting of the Association. 

That Dr. Carpenter be requested to draw up a Report on the Minute 
Structure of Shells. 

That Dr. Michael Foster be requested to report upon the Present State 
of our Knowledge in reference to Muscular Irritability. 

That Mr. James Oldham be requested to continue his Report on Steam 
Navigation in the Port of Hull. 

That the Lord Rosse, Dr. Robinson, Professor Phillips, and Mr. W. R. Birt 
be a Committee for the purpose of making observations on the Moon’s sur- 
face and comparing it with that of the Earth. That Professor Phillips be the 
Secretary. 

That the Rev. Professor Price, Dr. Whewell, Sir J. Lubbock, Admiral 
FitzRoy, Sir W. S. Harris, and Rey. Professor Haughton be a Committee for 
the purpose of reporting to the next Meeting of the British Association, on 
the Expediency and best means of making Tidal Observations, with a view 
to the completion of Dr. Whewell’s Essays in prosecution of a full Tidal 
Exposition. 

That, as it would be highly desirable that the observations on the Magnetic 
Lines in India should be continued, His Highness The Rajah of Travancore 
be requested to complete the Survey already commenced by him, through 
his Astronomer. 

That it is desirable that a Committee be appointed to consider the best 
mode of effecting the registration and publication of the numerical facts of 
Chemistry. That the Committee consist of Dr. Frankland, Dr. W. A. Miller, 
Prof. W. H. Miller, Prof. Brodie, Prof. Williamson, and Dr. Lyon Playfair. 

That the Lords of the Admiralty be moved to authorize some small vessel 
stationed on the South-East Coast of America to take a convenient oppor- 
tunity of collecting specimens of the large Vertebrate Fossils from certain 
localities easy of access between the River Plata and the Straits of 
Magellan. 

That Sir W. Jardine, Bart., Prof. Owen, Prof. Faraday, and Mr. Andrew 
Murray be a Committee for the purpose of procuring information as to the 
best means of conveying Electrical Fishes alive to Europe. That Sir W. 
Jardine be the Secretary. 

That Mr. William Fairbairn, Mr. J. F. Bateman, and Prof. Thomson be a 
Committee for .the purpose cf reporting on Experiments to be made at the 
Manchester Waterworks on the Gauging of Water; with power to add to 
their number. 


xl vill REPORT—1860. 


That the Committee to report on the Rise and Progress of Steam Naviga- 
tion in the Port of London be reappointed, and that the following gentlemen 
be requested to serve on it:—Mr. William Smith, C.E.; Sir John Rennie, 
F.R.S.; Captain Sir Edward Belcher; Mr. George Rennie, F.R.S.; Mr. Henry 
Wright, Secretary ; with power to add to their number. 


Involving Applications ta Government or Public Institutions. 


That the Parliamentary Committee, now consisting of the Duke of Argy!!. 
Dake of Devonshire, Earl de Grey, Lord Enniskillen, Lord Harrowby.’ 
Lord Rosse, Lord Stanley, Lord Wrottesley, Bishop of Oxford, Sir Philip 
Egerton, Sir John Packington, be requested to recommend two members of 
the House of Commons to fill the two vacancies. 

That Sir Roderick I. Murchison, as Trustee of the Association, and Mr. 
Nassau W. Senior, as President of the Section of Economie Science and Sta- 
tistics, be a Delegacy for the purpose of attending the International Sta- 
tistical Congress in London on July 16. 

That the Committee on Steam-ship Performance be requested to commu- 
nicate with the Parliamentary Committee, for the purpose of obtaining their 
assistance in accomplishing the objects for which the Committee on Steam- 
ships was appointed. 


Communications to be printed entire among the Reports. 


That the Communications by the Rev. W. V. Harcourt, on the results of 
Experiments at the Low Moor Iron Works, be printed entire among the 
Reports of the Association. 

That Mr. William Fairbairn’s Paper, on Experiments to determine the 
effect of vibratory action and long-continued changes ef load upon Wrought- 
iron Girders, be printed entire in the Reports of the Association. 

That Admiral Moorsom’s Paper, on the Performance of Steam Vessels, 
be printed entire among the Reports. 

That Mr. Elder’s Paper, on a cylindrical spiral boiler, with comparative 
evaporating power and temperatures of furnaces, flues and chimneys of 
various boilers, be printed entire in the Transactions of the Sections, with 
the necessary diagrams. 


Synopsis of Grants of Money appropriated to Scientific Objects by the 
General Committee at the Oxford Meeting in June and July 1860, 
with the name of the Member, who alone, or as the First of a Com- 
mittee, is entitled to draw for the Money. 


Kew Observatory. pee oe Da 

Kew Observatory Establishment ......... a Sth nie Sand Se nt OO ee 
Mathematical and Physical Science. 

Photo-heliographic Observations at Kew... .. eee. cece nece 90 0 O 

TYNDALL and Bati.—Alpine Ascents ........ eeeese008 10 0 O 


Carried forward i .% ccs cave cele vetenree alana 600 1) ) 


RECOMMENDATIONS OF THE GENERAL COMMITTEE, 


£ 
OOS i 2 es eee ere 600 
Balloon Committee ...... Li wee =e eer ye peme 0,0) 
Broun and Committee. —Dip- Bletlogh PA MEE cus sas 30 
Chemical Science, including Mineralogy. 
Marruatessen, Dr.—Chemical Alloys...........0 00.0 ee oe 20 
SuLtivan, Professor.—Solubility of Salts ............ meeps. 20 


VoeEtcker, Professor.—Constituents of Manures .......... 23 
Gaces, ALpHonse.—Chemistry of Rocks and Minerals .... 20 


Geology. 
Matter, Rosertr.— Earthquake Observations ............ 25 
Committee.—Excavations at Dura Den ..........00...+22 20 
Zoology and Botany. 

Jerrreys, J. G., and Committee—Ravages of Teredo and 

EMMI SISSY a 2 OND Pc deo ky 16 oA laid. ciara. bid'g/e 10 
Scrater, P. L., and Committee.—Report on Terrestrial Verte- 

brata of West PCS ae eee deals Sars mane bo Re es 10 


MacAnprew, R., and Committee.—For General Dredging .. 25 
Ocitvix, Dr., id Committee—Dredging the North and Rast 


Coasts of Scotland . eran 25 
JARDINE, Sir W., Bane mad Ooninilece. Revising iid Ret 
printing Rules of Zoological Nomenclature.............. 10 
ScLArEn, P: L.—Investigation of Apteryx..... sneha ie 50 
CoLiinewoop, Dr —Dredging i in Mersey aud: Dee, ss salt 5 
Physiology. 


Dr. Epwarp Smiru, F.R.S., and Mr. Mitner.—Effect of 
Prison Diet and Discipline upon the bodily functions of 
BN fe oh Pia Sool oh c'g'a’s sie, nce Cb rece eeveeeweene phatase 


Geography and Ethnology. 


Committee for exploring Uriconium...............-. sacs e 0) 
& Mechanical Science. 

Tuomsoy, Professor J.—Gauging of Water .......... 0008 10 

Committee on Steam-Ship Performance ......+.-... 0.0. 150 


Classified Index to the Transactions. 
Professor Patties (to employ an Assistant) ...........00+ 100 


Total,... £1395 O O 


xlix 


coooc 


oo 


Ores oso i=) 


0 


coos 


cook 


oosco 


oo 


OCS Osco 6S 


(6) 


1860. d 


REPORT—1860. 


General Statement of Sums which have been paid on Account of Grants for 


Scientifie Purposes. 
i 8s, - de £ 3. d. 
1834. Meteorology and Subterranean 
Tide Discussions ....escscceseeee 20 0 0 Temperature .......0ssssesceee ee 0 
1835 Vitrification Experiments........ ot) Ard 
Tide Di : y 62 0 0 Cast Iron Experiments...........+ 100 0 0 
Bete ce NS aiedeatnen se rar tyes Ae Railway Constants ....+.+0+... ses 28 
British Fossil Ichthyology .....- 10570) 70 Tid’ ond Sen Revel Ce agreed 
£167 0 0 | Steam-vessels’ Engines..,...- sees LOO. 20) 0 
1836 Stars in Histoire Céleste ...... .. 331 18 6 
F : : Stars in Lacaille .......00.....0 soe wile Way 
Tide Discussions .........seesesees 163 0 0 Stars in BOATS Gataleous 616 6 
British Fossil Ichthyology ...... 105) 0, ON ieee a apart BUS eaaies 10 10 0 
Thermometric Observations, &c. 50 0 0 Steamtonwines in Gordan ee 50 0 0 
Seba on Jong-continued 171.0 Atmospheric Air .........+0008 ee U6) Seg 
Rain Gauges ...ccesececeeeeees ccveee 913 0 by pH ete nies its . . : 
apenas fe ee Seep hs Cea Gases on Solar Spectrum ......... 22.0 0 
unar Nutation........-scee Poses OO MEO Ss (0 Hourly M lomenl On 
Thermometers . SCALE EC og, alii) ourly Breleoro On et ee 
aancneu sees Zucit |p es eS, and Kingussie es : 
OSS] Reptiles ..scscececcevereereee 
1837. Mining Statistics ........s000se000. 50 0 0 
Tide Discussions ....s..sseesesseee 284 1 O £1595 11.0 
Chemical Constants ....--...++ aes Met an G 
Tiunar Nutation\ ccccstrspostessenes 70 0 0 1840. 
Observations on Waves.........00+ 100 12 0 | Bristol Tides..........6. eeeves asaare L000) 70 
Tides at Bristol...cccccceccccccceces 150 © © | Subterranean Temperature ...... 13 13 6 
Meteorology and Subterranean Heart Experiments ,...0...s.s0008 18 19L 
Temperature ....scccccessssceeers 89 5 3 | Lungs Experiments ......+++.40 » 813 0 
Vitrification Experiments....... .. 150 0 0 | Tide Discussions .........++++94 + 50 0 0 
Heart Experiments .........0eesee 8 4 6 | Land and Sea Level............44 Vim Ui Sl 
Barometric Observations ......... 30 0 0 | Stars (Histoire Céleste) ......... 242 10 0 
IBALOMELETS Wavsesoeyoscsssescei se .» 11:18 6 | Stars (Lacaille) ......... COROCR 30 -» 415 0 
Bs Stars (Catalogue) ........006 weseacw 264 0 0 
eats 1438 Tae = ciseuesecs ececvevemn elo iO 
1838. Water on Iron .,....... anpupee eke eee 0: “10'-V6 
Tide Discussions ....ss...e0+8 eecse 29 © 0 | Heat on Organic Bodies ...... over! 0, De 20 
British Fossil Fishes ....... ses. 100 0 0 | Meteorological Observations...... 52 17 6 
Meteorological Observations and Foreign Scientific Memoirs ...... 1921.6 
Anemometer (construction)... 100 0 0 Working Population rest eee eeeee ees 100 0 0 
Cast Iron (Strength of) ...... wee 60 0 0 | School Statistics......ceeeeseerees ope at 
Animal and Vegetable Substances Forms of Vessels steeteeeeeeeeeenes 184 7 0 
(Preservation of) .......4. vateed 19 1 10 | Chemical and Electrical Pheno- 
Railway Constants ......... be 41 12 10 MENA . uc escececesecstesecesencescsn 40 0 0 
Bristol Tides .....sssseeeceeeeseereee 50 0 0 | Meteorological Observations at 
Growth of Plants ..... Re amen iene) Plymouth) ccescecsenss a exe ssenetens OOO 
Mudein URivers: csecssceecsentescevee 3 6 6 | Magnetical Observations ...,.,... 185 13 9 
Education Committee .......... 50 0 0 £1546 16 4 
Heart Experiments ............... 5 38 O ———— 
Land and Sea Level............0+ 267 8 7 1841. 
Subterranean Temperature ...... 8 6 0 | Observations on Waves...... seeeoO ONO 
Steam-vessels.........ses00+ cectecees 100 0 0O| Meteorology and Subterranean ‘ 
Meteorological Committee ...... Sp MOL Teel Temperature .......ssessees oe 882-0 
‘RHEYMIOMELErS iesassasessereasspanss 16 4 0 | Actinometers......ecssccssesseess 10 0 0 
£956 12 2 Earthquake Shocks .........scs0e 17 of eae, 
Se | Acrid Poisons...........0005 on siswiewa ~ 162 000 
1839. Veins and Absorbents .........4. - 38 0 0 
Fossil Ichthyology......... seve sates nl LOM OlaO VINTEC A GEUIVEES uneeesece ee acceses on 5. 0670 
Meteorological Observations at Marine Zoology.....sssseeesecees sos elie 2emrs 
Ply mottthiveecsae’eseesere eee sorte) 60010) 10))'SkeletonMapsi \.c.-..-nssc0seckeed a. 20% 02°10 
Mechanism of Waves ..........4- 144 2 0) Mountain Barometers ........... 5 GDL SiG 
Bristol Tides .....se.ssseeseseeseeeee 35 18 6 | Stars (Histoire Céleste)........0+ 185 0 0 


GENERAL STATEMENT. 


; 5 C5 aC 
Beare (Uacpille)Gosesecsscescsseecees 79 SB 10 
Stars (Nomenclature of) ......... 17. 19-.6 
Stars (Catalogue of) ...........0008 40 0 0 
eet ON) LOM esse kecescussesess as 50 0 0 
Meteorological Observations at 

DBEMRESS Eo npeccy ceccserensses tect 20 0 0 
Meteorological Observations (re- 
duction of) ..... miihspisesste sees 25> 7.0090 

Hossil Reptiles .......0..sessoseees we 504 0710 
Foreign Memoirs ..... Pseanes noses en O2ee0e G 
Railway Sections .......... eeResia 38 1 6 
Forms of Vessels ......0++.. Beesess 1938 12 0 
Meteorological Observations at 

EVTATOY Cll nays ceeeeyscre renee sss 55 0 0 
Magnetical Observations ......... 6118 8 
Fishes of the Old Red Sandstone 100 0 0 
Tides at Leith ...... Eabgasnss seats 50 0 0 
Anemometer at Edinburgh ...... 69 1 10 
Tabulating Observations ......... 96.33 
Races of Men  ....,..e0008 ero, ye Oe 
Radiate Animals ............ oye OLS 0 

£1235 10 11 

1842, 

Dynamometric Instruments ..,... 113 Ll 2 
Anoplura Britannie .....,. Aneta es Wee a 
Tides at Bristol............+6+ AAO Re Oe) ea 
Gases on Light..... Saracen ease oF BULA OF 
Chronometers ........... areanenaer 2help. (6 
Marine Zoology..........000+ recat wl aT RL, 
British Fossil Mammalia ....,.... 100 0 0 
Statistics of Education ........... Fie ZA eeel eat 
Marine Steam-vessels’ Engines... 28 0 0 
Stars (Histoire Céleste)............ 59 0 0 
Stars (Brit. Assoc. Cat. of) ...... 110 0 0 
Railway Sections .........sss000... 161 10 0 
British Belemnites...... “cohecocdcd 50 0 0 
Fossil Reptiles (publication of 

Report) .....,... Re eesee Shalt eld 0.40 
Forms of Vessels .........0 aon ses 180 0 0 
Galvanic Experiments on Rocks 5 8 6 
Meteorological Experiments at 

HAIGANIOUEN! 55 50¢.20rersccores ah 68 0 0 
Constant Indicator and Dynamo- 

metric Instruments ....... “oe LD UMD 
Force of Wind ............ cvececses 10 0 0 
Light on Growth of Seeds ...... ree MEL 
REAUSTALISLICS cayi..cssscesccesess fe D0 10-0 
Vegetative Power of Seeds ...... 8 1 11 
Questions on Human Race ...... 7 

£19 178 
1843. 
Revision of the Nomenclature of 

DETTE esse ccece sce RasedaTecsienne 6 Ate a 
Reduction of Stars, British Asso- 

ciation Catalogue ............00. 25 0 0 
Anomalous Tides, Frith of Forth 120 0 0 
Hourly Meteorological Observa- 

tionsat KingussieandInverness 77 12 8 
Meteorological Observations at 

MEP DOEN spaces eGeecwcsvieces ee dp” TOA 
Whewell’s Meteorological Ane- 

mometer at Plymouth .,....... 10 0 0 


Ge ons 
Meteorological Observations, Os- 
ler’s Anemometer at Plymouth 20 0 0 
Reduction of Meteorological Ob- 
SET VAtLONS Mew. .ssescecsecavenies we 30 0 0 
Meteorological Instruments and 
Gratuities Brceseujssesnseeiereetase Be Gi 
Construction of Anemometer at 
Inverness ....00+0- teeeeeeeeresens 5612 2 
Magnetic Co-operation ,,.......... 10 8 10 
Meteorological Recorder for Kew 
Observatory .......s000 ssesensvee 00 0 O 
Action of Gases on Light . eeseeece 18 16 1 
Establishment at Kew Observa- 
tory, Wages, Repairs, Furni- 
ture and Sundries ..........+5.06 1338 4 7 
Experiments by Captive Balloons 81 8 0 
Oxidation of the Railsof Railways 20 0 0 
Publication of Report on Fossil 
Reptiles .......+ Piereeousiscuseseey 40 0 0 
Coloured Drawings of Railway 
NEEHONSepewansarssasaveeersaresss 147 18 3 
Registration of Earthquake 
Shocks ...... aaRevesesesesathesers 30 0 0 
Report on Zoological Nomencla- 
tC Mises css on aspen snes bene® vores) 110/07 0 
Uncovering Lower Red Sand- 
stone near Manchester ......... 4 4 6 
Vegetative Power of Seeds ..... 5 3 8 
Marine Testacea (Habits of) ... 10 0 O 
Marine Zoology.....sssssseeees siege LDUGIES 
Marine Zoology....es.sseeceeseerace 2 14 11 
Preparation of*Report on British 
Fossil Mammalia .........00s.. - 100 0 0 
Physiological Operations of Me- 
dizinal:Agents si,cccsxesssorssse 120) 0) 0 
Vital Statistics ......sse.00 paeeecgs ND) ea 
Additional Experiments on the 
Horms:of Vesselsipeversssensses0 0 100 Ou 2 
Additional Experiments on the 
Forms of Vessels ....0s.ssss+000 100 0 0 
Reduction of Experiments on the 
Forms of Vessels ....ssseessee0s 100 0 0 
Morin’s Instrument and Constant 
Indicatot) seesse sake nestsaasasane ~» ) 628).14, 10 
Experiments on the Strength of 
Materials; po.esseressae BOcrecsecrem. 0) et MT 
£1565 10 2 
1844. 
Meteorological Observations at 
Kingussie and Inverness ...... 12 0 0 
Completing Observations at Ply- 
WAGUUG) wateyentenaaesercscaseses eon Ol 10 
Magnetic and Meteorological Co- 
OPETAUON Wasahaceescgscreeeesan - 25 8 4 
Publication of the British Asso- 
ciation Catalogue of Stars...... 35 0 0 
Observations on Tides on the 
East coast of Scotland ......... 100 0 0 
Revision of the Nomenclature of 
SEATS cans vecsacnetenn se sesexs 1842 2 9 6 
Maintaining the Establishment in 
Kew Observatory ......0...00 117 17 3 
Instruments for Kew Observatory 56 7 3 


d2 


lii REPORT—1860. 
a) ERAGE £ os. d. 
Influence of Light on Plants...... 10 0 0) Fossil Fishes of the London Clay 100 0 0 
Subterraneous Temperature in Computation of the Gaussian 
Treland) Wewerssadaessccestasstaee 5 0 0 Constants for 1839.......04+ sneer DORE OO 
Coloured Drawings of Railway Maintaining the Establishment at 
Sectionsineciscesocs teste dieorm esse 15 17 6 Kew Observatory ...scosseseeee . 146 16 7 
Investigation of Fossil Fishes of Strength of Materials....., asesyesns OO MO haO 
the Lower Tertiary Strata 100 0 0} Researches in Asphyxia........04- OP liGee 
Registering the Shocks of Earth- Examination of Fossil Shells...... 10 0 0 
CUUAIOS eine steels sslelvsisis cin ve 1842 23 11 10 | Vitality of Seeds .........00- 1844 2 15 10 
Structure of Fossil Shells ......... 20 0 0 | Vitality of Seeds ...,...0.... 1845 712 3 
Radiata and Mollusca of the Marine Zoology of Cornwall,..... 10 0 0 
ZSgean and Red Seas.....1842 100 0 0 | Marine Zoology of Britain ...... 10 0 0 
Geographical Distributions of Exotic Anoplura .secoe.eee 1844 25 0 0 
Marine Zoology........+++ 1842 010 0} Expensesattending Anemometers 11 7 6 
Marine Zoology of Devon and Anemometers’ Repairs ....++.. aod) 2 HOreEO 
Cornwall ........ssesesvevecesees 10 0 0} Atmospheric Waves .......se0ee.0e 3.3 3 
Marine Zoology of Corfu sesinees -«- 10 0 0) Captive Balloons ....... «1844 8S 19 3 
Experiments on the Vitality of Varieties of the Human Race 
GEUSlamecaaactcuusessiedsseseveddees 9 0 3 1844 7 6 38 
Experiments on the Vitality of Statistics of Sickness and Mor- 
Seedseetnecdiirarseterssaccecl GA eimOlr ot) oO tality in York ..,cccsscscensssase sla On 10 
Exotic Anoplura ......cssss0e0ce aetholion +10" 40 Fe685 1610) 
Strength of Materials .......... 100 0 0 ———— eee 
Completing Experiments on the 
Forms of Ships .....seeesereeeeee 100 0 0 : 1847. f 
Inquiries into Asphyxia ......... 10 0 0 | Computation of the Gaussian 
Investigations on the Internal So for 1882) RSS rorene 50 OOM 
Constitution of Metals ......... 50.0 ' 0 | Habits ee Sas sssaon 10 ae 
Gonctanuelidicatociandanioun's Physiological Action of Medicines 20 0 0 
Instrument, 1842 ...esseseeeee D0: 5 | eamne: Zeolasyol ComirallT an eae 
2 me i Ca Atmospheric Waves «sss... Peer ie Rs 
TSE ess MVatalityan SCCds. z.osedscnsensenees 4 7 7 
1845. Maintaining the Establishment at 
Publication of the British Associa- Kew Observatory svrsseeeseere 107 8 6 
tion Catalogue of Stars ....... 851 14 6 £208 5 4 
Meteorological Observations at 
Inverness ..... Sponpdoggcd: itacse’ 80.18 11 1848. 
Magnetic and Meteorological Co- Maintaining the Establishment at 
Operation... oe reneecenes vee 1616 8 Kew Observatory ssesssecessaees 171 15 11 
Meteorological Instruments at Atmospheric Waves ..sseesessees oot OS HORCS 
Edinburgh ....sccsvseees ieeneeaee 18 11 9] Vitality of Seeds ......ss00008 vat Da NO 
Reduction of Anemometrical Ob- Completion of Catalogues of Stars 70 0 0 
servations at Plymouth ........ 25 0 07} On Colouring Matters v.00. 5 0 0 
Electrical Experiments at Kew On Growth of Plants........0000.-- 15 0 O 
ObservatOry ...cecresssscseceass a AGL 28 £275.18 
Maintaining the Hatablishtacatn in ——— 
Kew Observatory aeaesaiaeemanes » 149 15. 0 
For Kreil’s Barometrograph ...... 25 000 F 1849, 
Gases from Iron Furnaces ...... 50 0 0 | Electrical Observations at Kew 
The Actinograph ....csscsessreeees ils ete Observatory sae eoy sents ousiccaniiey OO IO mel 
Microscopic Structure of Shells... 20 0 0 Maintaining Establishment at 
Exotic Anoplura s.sseecsee 1843 10 0 0 ditto serene aemieaitabicioie sists cosa) OMS 
Vitality of Seeds.....sssseesee 1843. 2 0 7 | Vitality of Seeds ws seeseees amu Brae 
Vitality of Seeds ...seeseeeee 1844 7 0 0 | OuGrowth of Plants..........+0+ 5 0 0 
Marine Zoology of Cornwall...... 10 0 | Registration of Periodical Phe- 
Physiological Action of Medicines 20 0 0 MOMENA seeeesseeseeneerserenee sees 10 0 0 
Statistics. of Sickness and More Bill on account of Anemometrical 
talitysin) York csstsspeeeeeeee 20 0 O| Observations ......... seeeeeweeens 139 0 
Earthquake Shocks ....... 1843 15 14 8 £159 19 6 
£330 9 9 
— 1850. 
1846. Maintaining the Establishment at 
British Association Catalogue of Kew Observatory ........ secesee 200 18 0 
Stars vsessceeevevsveveerereeet844 211 15 0 | Transit of Earthquake Wayes,.. 50 0 0 


GENERAL STATEMENT, 


ase es 

Periodical Phenomena .,.,........ 15 0 0 
Meteorological Instrument, 

AZOLES wesseseesceecsseenvenscears 2hmei0L. 0 


£345 18 0 


1851. 
Maintaining the Establishment at 
Kew Observatory (includes part 


of grantin 1849) .........ce0e0 309 2 2 
Theory of Heat ..........s0cee0 foe Pe MEA 
Periodical Phenomena of Animals 

MUDECIAUIES cy adaeseccccaseceacvece 5 0 0 
Vitality of Seeds ....cc.scsscereee 5 6 4 
Influence of Solar Radiation.,..... 30 0 0 
Ethnological Inquiries ..,......... 12 0 0 
Researches on Annelida ......... 10 0 0 

£391 9 7 
1852, 


Maintaining the Establishment at 

Kew Observatory (including 

balance of grant for 1850) ... 233 17 8 
Experiments on the Conduction 


PRMETEAC Tcadens nas -<ssescencas one. Lee 
Influence of Solar Radiations ... 20 0 0 
Geological Map of Ireland ..... Sapa Ol. 0 
Researches on the British Anne- 

11 Oca Ieeee Pree coresasn cece sdavseae £02.00 1'0 
Vitality of Seeds ........ ceacncvees 10 6 2 
Strength of Boiler Plates ......... Gi 10500 

£304 6 7 
1853. 
Maintaining the Establishment at 

Kew Observatory ..... “acbcknnee 165 0 0 
Experiments on the Influence of 

Solar Radiation............0.08. 15 0 0 
Researches on the British Anne- 

RS Eart tama seis Sia nce sis vsldelass op aieeids 10 0 0 
Dredging on the East Coast of 

EHUAN Gs cccycscesnosascetcesecosee 10)), 0,40 
Ethnological Queries ....... crea PL oy, Oigi0 

£205 0 0 
1854, 
Maintaining the Establishment at 

Kew Observatory (including 

balance of former grant) ...... 330 15 4 
Investigations on Flax ..........+8 11 0 0 
Effects of Temperature on 

Wrought Iron . .3..-..00000. eset OS r OL. 0 
Registration of Periodical Pha- 

nomena ...., e'elele nial sinisalelselo'si'e seo lO Om 0 
British Annelida .............00006 10 0 0 
Watalityrol Seeds) ..:.csscssese.+0 itu, io 
Conduction of Heat ............... 4 2 0 

£380 19 7 
1855. 
Maintaining the Establishment at 

Kew Observatory ...........2... 425 0 0 
Earthquake Movements ........ oe OREO 0 
Physical Aspect of the Moon...... 11 8 5 
Vitality of Seeds ............40. -- 10 7 11 
Mamonthe World.,...s.<c0s.00s 15 0 0 
Ethuological Queries ...... caceen Siento) 
Dredging near Belfast .4........ 4 0 0 

£480 16 4 


iti 


& s d. 
1856. 
Maintaining the Establishment at 
Kew Observatory :-— 
1854.....£ 75 0 0 
1855......£500 0 i: oer 88 
Strickland’s Ornithological Syno- 

TY MS cseclese pacha ae wamtandudanes vos 100 0.0 
Dredging and Dredging Forms... 913 9 
Chemical Action of Light........ 20 0 0 
Strength of Iron Plates............ 10 0 0 
Registration of Periodical Pheno- 

MMETA® waecleshenseaxeeee abi Beade ses 10 0 0 
Propagation of Salmon .seseeeeeee 10 0 0 

£754 13 9 
1857. 
Maintaining the Establishment at 

Kew Observatory sescsesesesees . 350 0 0 
Earthquake Wave Experiments 40 0 0 
Dredging near Belfast ....... seeicny item Onn O 
Dredging on the West Coast of 

Scotland......... tessa devsiciiasa 450 UA Ae 
Investigations into the Mollusca 

of California ......... caevacenoens 10 0 0 
Experiments on Flax ........... 5 0 O 
Natural History of Madagascar.. 20 0 O 
Researches on British Annelida 25 0 0 
Report on Natural Products im- 

ported into Liverpool ......... 10 0 0 
Artificial Propagation of Salmon 10 0 0 
Temperature of Mines ,.,... spa a me, 
Thermometers. for Subterranean 

Observations .esccessssseees Gearee (MeOE, nia’ 
Hife=B0dtsisrsssscecnncscadscrescssnestan (01 m0n 0 

£507 15 4 
1858. 
Maintaining the Establishment at 

Kew Observatory ........ sesease 000 0 
Earthquake Wave Experiments.. 25 0 
Dredging on the West Coast of 

Scotland — cevseressveveceees ida es 10 0 0 
Dredging near Dublin ........-.. AEC a 
Vitality of Seeds” ect ieccssseceee 5 5 0 
Dredging near Belfast ....+....40. 18 13 2 
Report on the British Annelida... 25 0 O 
Experiments on the production 

of Heat by Motion in Fluids... 20 0 0 
Report on the Natural Products 

imported into Scotland......... 10 0 0 

£518 18 2 
1859. 
Maintaining the Establishment at 

Kew Observatory ....+666 peeeessie O00 MeiOm nO 
Dredging near Dublin ..........46 15 0 0 
Osteology of Birds,......ssseseseree 50 0 0 
Trish Tunicata .....c.cscecsssesenes 5 0 OU 
Manure Experiments ......00+.0s 20 0 0 
British Medusid@ ...........se0e00e Sy 0220) 
Dredging Committee.......... aceboy Wa 
Steam Vessels’ Performance...... 5 0 0 
Marine Fauna of South and West 

Of Ireland ieecsncsnescave ss eaaesure 19 0 0 
Photographic Chemistry ......... 10 0 0 
Lanarkshire Fossils ....e..s.066 20 0 
Balloon’ AscentS.:cssjscrssseoeserees 09 11 1 

£684 11 1 


—_————EEEe 


liv REPORT—1860. 


1860. & s. d, & s. d. 
Maintaining the Establishment Researches on the Growth of 
of Kew Observatory ..........+0. S00 HO". 0 PJGWts. vscacee-.dacteccesveeteancede 10 0 0 
Dredging near Belfast..........++ 16 6 0 | Researches on the Solubility of 
Dredging in Dublin Bay........... 15 0 0 DHIES=sOistrassssuees-yscsomstersated 30 0 0 
Inquiry into the Performance of Researches on the Constituents 
Steam -vessels...csceseccseseseeeee 124 0 0 Of Manures ..........-csoceesvesoss 25 0 0 
Explorations in the Yellow Sand- Balance of Captive Balloon Ac- 
stone of Dura Den...........0066 20 0 O COUNES, .ccocsccvccscsccnssescocesers 113 6 
Chemico-mechanical Analysis of $1241 7 0 
Rocks and Minerals........s0+++ 25 0 0 areca! 


Extracts from Resolutions of the General Committee. 


Committees and individuals, to whom grants of money for scientific pur- 
poses have been entrusted, are required to present to each following meeting 
of the Association a Report of the progress which has been made; with a 
statement of the sums which have been expended, and the balance which re- 
mains disposable on each grant. 

Grants of pecuniary aid for scientific purposes from the funds of the Asso- 
ciation expire at the ensuing meeting, unless it shall appear by a Report that 
the Recommendations have been acted on, or a continuation of them be 
ordered by the General Committee. 

In each Committee, the Member first named is the person entitled to call 
on the Treasurer, John Taylor, Esq., 6 Queen Street Place, Upper Thames 
Street, London, for such portion of the sum granted as may from time to 
time be required. 

In grants of money to Committees, the Association does not contemplate 
the payment of personal expenses to the members. 

In all cases where additional grants of money are made for the continua- 
tion of Researches at the cost of the Association, the sum named shall be 
deemed to include, as a part of the amount, the specified balance which may 
remain unpaid on the former grant for the same object. 


General Meetings. 

On Wednesday, June 27, at 4 p.m., in the Sheldonian Theatre, His Royal 
Highness, the Prince Consort, resigned the office of President to The Lord 
Wrottesley, F.R.S., who took the Chair and delivered an Address, for which 
see page lv. 

On Thursday Evening, June 28, at 85 p.M., a Conversazione took place in 
the University Museum. 

On Friday Afternoon, June 29, at 4 p.m., in the Sheldonian Theatre, the 
Rev. Professor Walker, F.R.S., delivered a Discourse on the Physical Con- 
stitution of the Sun. 

On Friday Evening, the University Museum was opened for a Soirée with 
Experiments. 

On Monday Afternoon, July 2, at 2 p.m., in the Sheldonian Theatre, 
Captain Sherard Osborn, R.N., delivered a Discourse on Arctic Discovery. 

On Monday Evening, at 8} pP.m., a Conversazione took place in the 
University Museum. 

On Tuesday Evening, July 3, at 8} p.m., the University Museum was 
opened for a Soirée with Microscopes. 

On Wednesday, July 4, at 3 p.m., the concluding General Meeting took 
place in the Sheldonian Theatre, when the Proceedings of the General Com- 
mittee, and the Grants of Money for Scientific purposes, were explained to 
the Members. 

The Meeting was then adjourned to Manchester*. 


* The Meeting is appointed to take place on Wednesday, the 4th of September, 1861. 


ADDRESS 
BY 


THE RIGHT HON. THE LORD WROTTESLEY. 


GENTLEMEN,—If, on taking this Chair for the first time as your President, 
I do not enlarge upon my deficiencies for adequately filling the responsible 
office to which you have done me the honour to elect me, I hope you will 
believe that I am not the less sensible of them. 

Your last Meeting was held under the Presidency of one not more distin- 
guished by his high rank and exalted station than by his many excellent 
qualities, and the discriminating interest which he has ever manifested in the 
promotion of Art and Science. It was one of the most successful Meetings on 
record. 

We are now once more assembled in this ancient and venerable seat of 
learning ; and the first topic of interest which presents itself to me, who owe 
to Oxford what academic training I have received, is the contrast presented 
by the state of Science and the teaching of Science in this University in the 
Autuinn of the year 1814, when my residence here commenced, and for five 
years alterwards, with its present condition. As the private pupil of the late 
Dr. Kidd, and within a few yards of the spot from which I have now the honour 
to inaugurate the Meeting of this distinguished Association, I first imbibed 
that love of Science from which some of the purest pleasures of my life have 
been derived ; and I cannot mention the name of my former Tutor without 
acknowledging the deep debt of gratitude I owe to the memory of that able, 
conscientious and single-hearted man. 

It was at this period that a small knot of Geologists, headed by Broderip, 
Buckland, the two Conybeares and Kidd, had begun to stimulate the curiosity 
of the Students and resident Graduates by Lectures and Geological excur- 
sions in the neighbourhood of this town. The lively illustrations of Buck- 
land, combined with genuine talent, by degrees attracted crowds to his 
teaching, and the foundations of that interesting science, already advancing 
under the illustrious Cuvier in France, and destinedsoon to spread over Europe, 
were at this time fairly laid in England within these classical Halls. Many 
atime in those days have my studies been agreeably interrupted by the 


lvi REPORT—1860. 


cheerful laugh which invariably accompanied the quaint and witty terms in 
which Buckland usually announced to his brother Geologist some new dis- 
covery, or illustrated the facts and principles of his favourite science. At 
the time, however, to which I refer, the study of physical science was chiefly 
confined to a somewhat scanty attendance on the Chemical Lectures of Dr. 
Kidd, and on those on Experimental Philosophy by Rigaud; and in pure 
mathematics the fluxional notation still kept its ground. In the year 1818 
Vince’s Astronomy, and in the following year the Differential Notation, was first 
introduced in the mathematical examinations for honours. At that time 
that fine foundation the Radcliffe Observatory was wholly inactive; the 
observer was in declining health, and the establishment was neither useful to 
astronomical students, nor did it contribute in any way to the advancement 
of Astronomical Science. Even from the commencement of the present 
century, and in proportion as the standard of acquirement in classical learning 
was gradually raised by the emulation excited by the examinations for 
honours, the attendance on the above-mentioned Lectures gradually declined : 
but a similar cause enhanced the acquirements of students in pure and 
applied Mathematics, and the University began to number among its 
Graduates and Professors men of great eminence in those departments of 
knowledge. Nor were the other sciences neglected ; and as Chairs became 
vacant or new Professorships were established, men of European reputation 
were appointed to fill them. In proof of all this I need only direct. atten- 
tion to the names on the roll of Secretaries, Vice-Presidents and Presidents 
of Sections, to convince you that Oxford now contains among her resident 
Graduates, men amply qualified to establish and advance the scientific fame 
of that University, of which they are the distinguished ornaments. 

On the progress of Astronomy I will, as becomes me, enter into more 
detail, And it is not without pain that I allude to this subject, because I am 
reminded that one has been removed from among us by the hand of death, 
whom I had looked forward to meeting again on this occasion with peculiar 
pleasure. I never knew any one who had the interests of science more truly 
at heart, or laboured more diligently to advance them, than the late Radcliffe 
Observer, Mr. Manuel Johnson. ; By his exertions and indefatigable zeal 
the Radcliffe Observatory was enabled.to take its proper place among the 
Scientific Institutions of the world. By the liberality of the Trustees and 
by the exertion of his influence, new instruments were purchased, and an 
extensive series of valuable astronomical observations was made; and, what 
is quite as important, they were regularly reduced and published. In addi- 
tion to all this, a noble array of self-recording meteorological instruments was 
brought into action, and their records duly reduced and co-ordinated. I was 
nyself a candidate in 1839 for that office to which Mr. Johnson was then 
appointed, and I have often rejoiced that I was not successful, as it would 
have retarded for a time the promotion of one, to whom Astronomy owes a 
deep debt of gratitude. Mr. Johnson was suddenly taken from us at a time 


ADDRESS. vii 


when he was in the full career of his useful labours, and there are few 
Jabourers in science whose loss has been more deplored. The University has 
very lately lost another learned Professor, and myself another valued friend, 
whose contributions to science are well known and duly esteemed. The 
great tragic Poet of Greece introduces his hero accusing his heathen gods 
of rescuing from the grave the vile and worthless, and sending thither the 
good and useful :— 

seers TH OG Oikata Kal Ta xpnoTa 

amrooréAXovaty aéi. 
Our purer faith in meek resignation trusts that they are removed from evil 
to come, and that there at least they rest from their labours—rest from 
earthly toil and trouble, but awake, may be, to higher aims and aspirations, 
and with nobler faculties and duties. 

Although a successor may be appointed to Mr. Johnson, who will, I doubt 
not, admirably discharge the duties of Radcliffe Observer, I fear that the 
Observatory may not continue to maintain its high reputation, unless a suffi- 
cient staff of Assistants be appointed to aid the Observer in his labours. 
There is no mistake more fatal in Astronomy than that of multiplying in- 
strumental means without providing an adequate supply of hands to employ 
them. 

I have already alluded to some particulars in which this great University 
has advanced in the career of scientific improvement, but everything else has 
been somewhat thrown into the shade by the important event of this year, 
the opening of the new Museum. The University could have given no more 
substantial proof of a sincere interest in the diffusion of science than the 
foundation of this noble Institution, and I am sure that among the distin- 
guished cultivators of science here assembled, there is not one who does not 
entertain a hearty desire for the success of the various effurts now in progress 
for the purpose of stimulating our University Students to a closer contempla- 
tion and more diligent study of the gloricus works of Nature; a study, which, 
if prosecuted earnestly, raises us in the scale of human beings and improves 
every moral and intellectual faculty. Towards the attainment of a result so 
much to be desired the Museum will most powerfully contribute, and those 
who frequent it will owe deep obligations to Mr. Hope and the other bene- 
factors who have generously added to its stores. But there are other causes 
in operation which tend to the same end; and among them, in addition to 
such improvements as arise out of the changes consequent on the recent 
Act of Parliament, may be mentioned the alteration in the distribution of 
Dniversity Honours. 

The institution of the School of Physical Science forms a most important 
feature in the recent changes, and will doubtless be productive of good results, 
provided that sufficient encouragement by way of reward be held out to 
those whose tastes lead them to devote themselves to those departments of 
knowledge, and that the compulsory arrangements in respcet of other studies 


lvili REPORT—1860. 


allow sufficient time to the student to accomplish his object. The great 
majority of physical students must necessarily belong to that class who have 
their subsistence to earn ; and however earnest may be their zeal for mental 
improvement, there will be few candidates for the honours of the Physical 
School unless due encouragement be given to excellence in that department. 
It was therefore with sincere pleasure that I learnt that three Fellowships 
had been founded at Magdalen College as prizes for proficiency in Natural 
Science; and that at the same College, and at Christ Church and Queen’s, 
Scholarships and Exhibitions had been provided for students who evince 
during their examinations the greatest aptitude for such studies. Moreover, 
the acquisition of a Radcliffe travelling Fellowship has been made to depend 
upon obtaining distinction in the School of Natural Science. In addition to 
all this, that beneficent and enlightened lady, Miss Burdett Coutts, has founded 
two Scholarships with the view of extending among the Clergy educated at 
the University a knowledge of Geology. Great hopes are justly excited in 
the minds of all well-wishers to the University by these events, and by reflec- 
tion on the great change of opinion which must have taken place since the 
period when Dr. Kidd, with the aid of Dr. Daubeny, Mr. Greswell and others, 
in vain attempted to raise a small sum by private subscription for building a 
modest receptacle for the various collections of Natural History. How little 
could these public-spirited individuals have foreseen, that within a few short 
years a sum approaching to £100,000 would be appropriated to the building 
and furnishing that splendid monument of Oxford's good will to science, the 
New Museum ! 

It would not be right, however, if, while speaking in just and sincere terms 
of praise of all that excites my admiration in the late proceedings at Oxford, 
I were to withhold the honest expression of my opinion on points on which 
I feel compelled to differ from the course pursued. I will therefore refer to 
two measures, one of which especially I cannot but regard as a mistake, 
The first is the repeal of the statute which enforced attendance on two courses 
of Professorial lectures ; a requirement, which may have had no small influ- 
ence in creating a taste for natural science among that large class of students, 
whose only object it is to obtain, in a creditable manner if possible, but at all 
events to obtain, the distinction of an Academical degree. At the same time 
I cannot but be sensible that the amount of instruction imparted in this way, 
even if the attendance were much more than nominal, must necessarily have 
been small, not from any want of competency in the teachers, but from the 
inherent defect of the system of lectures unaccompanied by examinations ; 
and on this account I the less regret the change. 

The second, and more serious mistake, in my humble opinion, is the re- 
jection by the Congregation in 1857 of the proposal of the Hebdomadal 
Council, that the Undergraduate, after passing his first two classical exami- 
nations, should be permitted to select his own line of study, and submit 
himself at his option to a final examination in any one of the four Schools, 


ADDRESS. lix 


that is, the Classical, the Mathematical, History and Law, or Natural Science. 
The Hebdomadal Council were I think right in believing that such mental 
discipline as classical study can impart—and far be it from me to undervalue 
it in the least—would be sufficiently secured by the classical requirements of 
the two first examinations; aud that the study of Mathematics and the Natural 
Sciences, besides imparting much valuable information, which might be exten- 
sively utilized in after-life, might equally be viewed as an important means 
of improving the intellectual faculties. There is another consideration which 
must not be lost sight of in deciding on the policy of the course then pursued. 
I think that it cannot in fairness be expected that a young man of the average 
abilities of those who contend for honours, and who is called upon to pass 
two classical examinations, and prepare for a third, before he is allowed to 
follow the bent of his genius and apply himself to his favourite study, can 
find time to attain a sufficient proficiency in it to pass a really creditable 
examination ; accordingly the necessary result will be that the Examiners will 
be obliged to lower the standard of honour, the rather that most of the students 
now come to the University without having acquiredeventheelements of scien- 
tific knowledge, and thus the first class may almost cease to be a distinction 
worth attainment. 

I cannot take leave of recent University changes without adverting to that 
great, that noble step, the institution of the Middle Class Examinations, 
whereby Oxford has furnished substantial aid to those more humble aspirants 
to knowledge, by whom a University education, however much desired, is 
quite unattainable. Whether this movement be viewed in its moral effect, as 
showing a kindly sympathy of the higher intellectual class with the struggling 
but deserving children of a lower sphere, or as the best expedient for bringing 
about a complete reform in our educational establishments, and therefore a 
great engine for advancing popular education—whether this grand and 
liberal step be viewed in one or both these aspects, it has given the most 
unmixed and heartfelt satisfaction to all who have the moral and mental 
improvement of the nation sincerely at heart; and greatly do I rejoice that 
such a satisfactory proof should have been given of a desire to make Uni- 
versity Institutions a general national blessing. 

Oxford, then, has shown herself fully equal to her glorious mission, and it 
was only a fitting sequel to such enlightened conduct, that she should be 
entrusted with the grateful task of educating the Heir apparent to the Throne 
of the most popular Sovereign who ever swayed the sceptre of this vast 
_ Empire. 

I shall perhaps be forgiven if my former connexion with Oxford, and the 
interest which I must ever take in everything appertaining to my own Uni-. 
versity, have induced me to dwell somewhat at length on the above matters. 
It is now time that I should direct my attention to the general domain of 
science ; but more particularly to that department to which my own labours, 
humble though they be, have been more especially devoted,—I mean the 


Ix REPORT—1860. 


science of Astronomy, a science, which, whether we consider the surpassing 
interest of the subjects with which it is conversant, or tbe lofty nature of the 
speculations to which its inquiries lead, must ever occupy a most distinguished, 
if not the first place among all others. 

In a discourse addressed in May 1859 to the Imperial Academy of 
Sciences of Vienna, by the distinguished Astronomer Littrow, a very full ac- 
count is given of the voluntary contributions of the private observers of 
all nations to the extension of the science of Astronomy ; and this discourse 
concludes with a remarkable sentence, of which our English Amateurs may 
well be proud: he expresses a hope that on the next occasion in which he 
shall be called upon to dilate on the same theme, he shall not as then have 
to mention English names in such preponderating numbers. 

At the beginning of the year 1820, when the Astronomical Society was 
founded, the private Observatories in this country were very few in number. 
The establishment of that Society gave a most remarkable stimulus to the 
cultivation of the science which it was intended to promote. 1 can give no 
better proof of this than the fact thatthe Nautical Almanac now contains a 
list of no less than twelve private Observatories in the United Kingdom, at 
nearly all of which some good work has been done; and in addition to this, 
some Observatories, which have been since discontinued, have performed most 
important services—I may instance that of the two Herschels at Slough, and 
that of Admiral Smyth at Bedford. 

It may not be uninteresting if I describe the nature and utility of some 
of the results which these several establishments have furnished to the world: 
I say the world advisedly, for scientific facts are the common inheritance of 
all mankind. 

But first a werd as to the peculiar province of the observatories which are 
properly called ‘ public,” such as the far-famed Institution at Greenwich. 
Their task is now more peculiarly to establish with the last degree of accu- 
racy the places of the principal heavenly bodies of our own system, and of 
the brighter or fundamental fixed stars, which are about 100 in number. 
But in the early stages of Astronomy, we were necessarily indebted to public 
Observatories for all the data of the science. On the other hand, their vo- 
luntary rivals occupy that portion of the great astronomical field which is 
untilled by the professional observer; roving over it according to their own 
free will and pleasure, and cultivating with industrious hand such plants as 
the more continuous and severe labours of the public Astronomer leave no 
time or opportunity to bring to maturity. 

The observations of our private observers have been chiefly devoted to 
seven important objects :— 

First. The observing and mapping of the smaller stars, under which term 
I include all those which do not form the peculiar province of the public 
observer. 

Secondly. The observations of the positions and distances of double stars. 


ADDRESS. Xl 


Thirdly. Observations, delineations, and Catalogues of the Nebule. 

Fourthly. Observations of the minor planets. 

Fifthly. Cometary observations. 

Sixthly. Observations of the solar spots, and other phenomena on the 
Sun’s disc. 

Seventhly. Occultations of stars by the Moon, eclipses of the heavenly 
bodies, and other occasional extra-meridional observations. 

And first as to cataloguing and mapping the smaller stars. This means, 
as you know, the accurate determination by astronomical observation of the 
places of those objects, as referred to certain assumed fixed points in the 
heavens. The first Star Catalogue worthy to be so called, is that which goes 
by the name of Flamsteed’s, or the British Catalogue. It contains above 
$000 stars, and is the produce of the labours of the first Astronomer Royal 
of Greenwich, labours prosecuted under circumstances of great difficulty, 
and the results of which were not given to the world in a complete form till 
many years had elapsed from the time the observations were made, which 
was during the latter half of the seventeenth century. About the middle 
of the eighteenth century, the celebrated Dr. Bradley, who also filled the post 
of Astronomer Royal, observed an almost equally extensive Catalogue 
of Stars, and the beginning of the nineteenth century gave birth to that of 
Piazzi of Palermo. These three are the most celebrated of what may be 
now termed the ancient Catalogues. About the year 1830 the attention of 
modern astronomers was more particularly directed to the expediency of re- 
observing the stars in these three Catalogues, a task which was much faci- 
litated by the publication of a very valuable work of the Astronomical 
Society, which rendered the calculations of the observations to be made com- 
paratively easy, and accordingly observations were commenced and com- 
pleted in several public and private Observatories, from which some curious 
results were deduced, as e. @., sundry stars were found to be missing, and 
Others to have what is called proper motion. And now a word as to the 
utility of this course of observation. It is well observed by Sir John 
Herschel, “ that the stars are the landmarks of the Universe; every well-deter- 
mined star is a point of departure which can never deceive the astronomer, 
geographer, navigator, or surveyor.” We must have these fixed points in 
order to refer to them all the observations of the wandering heavenly bodies, 
the planets and the comets. By these fixed marks we determine the situation 
of places on the earth’s surface, and of ships on the ocean. When the places of 
the stars have been registered, celestial charts are constructed ; and by com- 
paring these with the heavens, we at once discover whether any new body 
be present in the particular locality under observation: and thus have most 
of the fifty-seven small or minor planets between Mars and Jupiter been 
discovered. ‘Ihe observations, however, of these smaller stars, and the re- 
gistry of their places in Catalogues, and the comparisons of the results ob- 
tained at different and distant periods, have revealed another extraordinary 


Ixii REPORT—1860. 


fact, no less than that our own Sun is not fixed in space, but that it is con- 
stantly moving forward towards a point in the constellation Hercules, at the 
rate, as it is supposed, of about 18,000 miles an hour, carrying with it the 
whole planetary and cometary system; and if our Sun moves, probably all 
the other stars or suns move also, and the whole universe is in a perpetual 
state of motion through space. 

The second subject to which the attention of private observers has been 
more particularly directed, is that of double or multiple stars, or those which, 
being situated very close to one another, appear single to the naked eye, but 
when viewed through powerful telescopes are seen to consist of two or more 
stars. The measuring the angles and distances from one another of the two 
or more component stars of these systems, has led to the discovery that many 
of these very close stars are in fact acting as suns to one another, and revol- 
ving round their common centre of gravity, each of them probably carrying 
with it a whole system of planets and comets, and perhaps each carried for- 
ward through space like our own sun. It became then a point of great in- 
terest to determine, whether bodies so far removed from us as these systems, 
observed Newton’s law of gravity, and to this end it was necessary to observe 
the angles and distances of a great number of these double stars scattered 
everywhere through the heavens, for the purpose of obtaining data to com- 
pute their orbits. This has been done, and chiefly by private observers; and 
the result is that these distant bodies are found to be obedient to the same 
laws that prevail in our own system. : 

The Nebulz are, as it were, systems or rings of stars scattered through space 
at incredible distances from our star system, and perhaps from one another; 
and there are many of these mysterious clouds of light, and there may be 
endless invisible regions of space similarly tenanted. Now the nearest fixed 
star of our star system whose distance has been measured, is the brightest in the 
constellation Centaur, one of the Southern constellations, and this nearest is 
yet so far removed, that it takes light, travelling at the rate of about 192,000 
miles per second, three years to arrive at the earth from that star. When 
we gaze at it, therefore, we see it only as it existed three years ago; some 
great convulsion of nature may have since destroyed it. But there are many 
bright stars in our own system, whose distance is so much greater than this, 
as a Cygni, for example, that astronomers have not succeeded in measuring it. 
What, then, must be the distance of these nebule, with which so much space 
is filled; every component star in which may be a sun, with its own system 
of planets and comets revolving round it, each planet inhabited by myriads 
of inhabitants! What an overpowering view does this give us of the extent 
of creation! The component stars of these nebulz are so faint and appa- 
rently so close together, that it is necessary to use telescopes of great power, 
and with apertures so large as to admit a great amount of light, for their ob- 
servation. We owe it more especially to four individuals, that telescopes 
have been constructed, at a great cost and with great mechanical skill, suf- 


ADDRESS. xiii 


ficiently powerful to penetrate these depths of space. Those four indivi- 
duals are the Herschels, father and son, Lord Rosse, and Mr. Wm. Lassell. 
That praiseworthy nobleman, Lord Rosse, began his meritorious career by 
obtaining a First Class at this University, and has, as you know, spent large 
sums of money and displayed considerable mechanical genius in erecting, 
near his own Castle in Ireland, an instrument of far greater power than any 
other in the world; and with it he has observed these nebule, and employed 
skilful artists to delineate their forms: and he has moreover made the very 
curious discovery, that some of them are arranged ina spiral form, a fact 
which gives rise to much interesting speculation on the kind of forces by 
which their parts are held together. It were much to be wished that obser- 
vations similar to these, and with instruments of nearly the same power, 
should be made of the Southern nebule also; that this generation might 
be able to leave to posterity a record of their present configurations. The 
distinguished Astronomer, Mr. Wm. Lassell, the discoverer of Neptune’s 
satellite, has just finished at his own cost an instrument equal to the task, 
mounted equatorially; and I am not without hope that it may, at perhaps 
no very distant period, be devoted to its accomplishment. A recent com- 
munication from him to the Astronomical Society expresses satisfaction with 
the mounting of his instrument, and after many trials its great speculum has 
at last come forth nearly perfect from his laboratory. 

I am, however, warned by the lapse of time, that it will not be possible for 
me to exhaust the whole field, the limits of which I have sketched, in which 
private enterprise has been assiduously at work to enlarge the bounds of 
astronomical knowledge. I will therefore pass at once to the two most in- 
teresting subjects which remain, the observations of Comets, and of peculiar 
appearances on the Sun’s disc. 

Of all the phenomena of the heavens, there are none which excite more 
general interest than comets, those vagrant strangers, the gipsies as they 
have been termed of our solar system, which often come we know not whence, 
and at periods when we least expect them: and such is the effect produced 
by the strangeness and suddenness of their appearance, and the mysterious 
nature of some of the facts connected with them, that while in ignorant times 
they excited alarm, they now sometimes seduce men to leave other employ- 
ments and become Astronomers. Now, though the larger and brighter 
comets naturally excite most general public interest, and are really valuable 
to astronomers, as exhibiting appearances which tend to throw light on the 
internal structure of these bodies, and the nature of the forces which must 
be in operation to produce the extraordinary phenomena observed, yet some 
of the smaller telescopic comets are, perhaps, more interesting in a physical 
point of view. Thus the six periodical comets, the orbits of which have been 
determined with tolerable accuracy, and which return at stated intervals, are 
extremely useful as being likely to disclose facts, of which but for them we 
should possibly have ever rernained ignorant. Thus, for example, when the 


Ixiv REPORT—1860. ; 


comet of Encke, which performs its revolution in a period of a little more than 
three years, was observed at each return, it disclosed the important and unex- 
pected fact, that its motion was continually accelerated. At each successive 
approach to the Sun it arrives at its perihelion sooner and sooner ; and there 
is no way of accounting for this so satisfactory as that of supposing that the 
space, in which the planetary and cometary motions are performed, is every- 
where pervaded by a very rarefied atmosphere or ether, so thin as to exercise 
no perceptible effect on the movements of massive solid bodies like the planets, 
but substantial enough to exert a very important influence on more attenuated 
substances moving with great velocity. ‘The effect of the resistance of the 
ether is to retard the tangential motion, and allow the attractive force of 
gravity to draw the body nearer to the Sun, by which the dimensions of the 
orbit are continually contracted and the velocity in it augmented. The final 
result will be that after the lapse of ages this comet will fall into the Sun; 
this body, a mere hazy cloud, continually flickering as it were like a celestial 
moth round the great luminary, is at some distant period destined to be mer- 
cilessly consumed. Now the discovery of this ether is deeply interesting as 
bearing on other important physical questions, such as the undulatory theory 
of light; and the probability of the future absorption of comets by the Sun 
is important as connected with a very interesting speculation by Professor 
William Thomson, who has suggested that the heat and light of the Sun may 
be from time to time replenished by the falling in and absorption of count- 
less meteors which circulate round him; and here we have a cause revealed 
which may accelerate or produce such an event. 

In the progress of science it often happens that a particular class of obser- 
vations, all at once, and owing to some peculiar circumstance, attracts very 
general attention and becomes deeply interesting. This has been the case 
within the last few years in reference to observations of the Sun's dise, which 
were at one time made by very few individuals, and were indeed very much 
neglected both by professional and amateur Astronomers. During this sea- 
son of comparative neglect, there were not, however, wanting some enthusiastic 
individuals, who were in silence and seclusion obtaining data of great import- 


ance. 
On the 1st of September last, at 118 18™ a.M., a distinguished Astronomer, 


Mr. Carrington, had directed his telescope to the Sun, and was engaged in 
observing his spots, when suddenly two intensely luminous bodies burst into 
view on its surface. They moved side by side through a space of about 
35,000 miles, first increasing in brightness, then fading away; in 5 minutes 
they had vanished. They did not alter the shape of a group of large black 
spots which lay directly in their paths. Momentary as this remarkable phe- 
nomenon was, it was fortunately witnessed and confirmed, as to one of the 
bright lights, by another observer, Mr. Hodgson at Highgate, who by a 
happy coincidence had also his telescope directed to the great luminary at 
the same instant. It may be, therefore, that these two gentlemen have 


ADDRESS. Ixv 


actually witnessed the process of feeding the Sun, by the fall of meteoric 
matter; but however this may be, it is a remarkable circumstance, that the 
observations at Kew show that on the very day, and at the very hour and 
minute of this unexpected and curious phenomenon, a moderate but marked 
magnetic disturbance took place; and a storm or great disturbance of the 
magnetic elements occurred four hours after midnight, extending to the 
southern hemisphere. Thus is exhibited a seeming connexion between mag- 
netic phenomena and certain actions taking place on the Sun’s disc—a con- 
nexion, which the observations of Schwabe, compared with the magnetical 
records of our Colonial Observatories, had already rendered nearly certain. 
The remarkable results derived from the comparison of the magnetical 
observations of Captain Maguire on the shores of the Polar Sea, with the 
contemporaneous records of these observatories, have been described by me 
on a former occasion. The delay of the Government in re-establishing the 
Colonial Observatories has hitherto retarded that further development of the 
magnetic laws, which would doubtless have resulted from the prosecution of 
such researches. 

We may derive an important lesson from the facts above alluded to. 
Here are striking instances in which independent observations of natural 
phenomena have been strangely and quite unexpectedly connected together : 
this tends powerfully to prove, if proof were necessary, that if we are really 
ever to attain toa satisfactory knowledge of Nature’s laws, it must be accom- 
plished by an assiduous watching of all her phenomena, in every department 
into which Natural Science is divided. Experience shows that such obser- 
vations, if made with all those precautions which long practice combined 
with natural acuteness teaches, often lead to discoveries, which cannot be at 
all foreseen by the observers, though many years may elapse before the 
whole harvest is reaped. 

I cannot allude to the subject of Arctic voyages without congratulating 
the Association on the safe return of Sir Leopold M‘Clintock and his gallant 
band, after accomplishing safely and satisfactorily the object of their inter- 
esting mission. The great results accomplished with such small means, and 
chiefly by the display of those qualities of indomitable courage, energy and 
perseverance which never fail the British seaman in the hour of need, are the 
theme of general admiration ; but I may be permitted in passing to express 
some regret, that it was left to the devoted affection of a widowed lady, 
slightly aided by private contributions, to achieve a victory in which the 
honour of the nation was so largely involved,—the rather that the danger of 
the enterprise,—the pretext for non-interference—was much enhanced 
thereby, and the accessions to our scientific and geographical knowledge 
proportionably curtailed. 

The instances to which I have alluded are only a few of many which 
could be adduced of an insufficient appreciation of certain objects of 
scientific research. Large sums are expended on matters connected 

e 


lxvi REPORT—1860. 


with science, but this is done on no certain and uniform system; and 
there is no proper security that those who are most competent to give good 
advice on such questions, should be the actual persons consulted. It was 
partly with the hope of remedying these defects and of generally improving 
the position of science in the country in its relation to the Government, that 
the Parliamentary Committee of this Association was established; and it 
was partly with the same hope that I was induced to accept the honourable 
office of President of the Royal Society, though conscious at the time that 
there were very many far better qualified than myself to hold it. Many of 
those whom I am now addressing are aware of the steps which were adopted 
by the Parliamentary Committee, and subsequently by the Committee of 
Recommendations of this Association, for the purpose of collecting the 
opinions of the cultivators of science on the question,—- Whether any measures 
could be adopted by Government or Parliament that would improve our 
position? The question was afterwards referred to and discussed by thie 
Council of the Royal Society, who, on the 15th of January, 1857, agreed 
upon twelve resolutions in reply thereto. These resolutions recommend, 
among other things, that Government grants in aid of local funds should be 
applied towards the teaching of science in schools, the formation of Provincial 
Museums and Libraries, and the delivery of lectures by competent persons, 
accompanied by examinations; and finally, that some existing scientific body, 
or some Board to be created for the purpose, should be formally recognized, 
which might advise the Government on all matters connected with science, 
and especially on the prosecution, reduction, and publication of scientific 
researches, and the amount of Parliamentary or other grants in aid thereof ; 
also on the general principles to be adopted in reference to public scientific 
appointments, and on the measures necessary for the more general diffusion 
of a knowledge of physical science among the nation at large; and which 
might also be consulted by the Government on the grants of pensions to the 
cultivators of science. 'I was requested to transmit these resolutions to Lord 
Palmerston, and also to the Parliamentary Committee of this Association. 
Since that period these resolutions have been discussed by that Committee ; 
but partly because some of its most influential members have expressed 
grave doubts as to the expediency of urging their adoption at all, and partly 
from the want of a favourable opportunity for bringing them forward, nothing 
further has as yet been done. I thought, however, that the time was arrived 
at which it was only proper that I should explain the steps which had been 
already taken, and the actual position in which the question now stands. If 
it be true, as some of our friends imagine, that the recognition of such a body 
as has been above described, however useful it might prove if the public 
were disposed to put confidence in its suggestions, would only augment that 
feeling of jealousy which is disposed to view every application for aid to 
scientific research in the light of a request for some personal boon, to be 
bestowed on some favoured individual, then indeed its institution would not 


—" 


ADDRESS. Ixvil 


be expedient. I only wish that persons who entertain such views, would pay 
some attention to the working of the Government Grant Committee of the 
Royal Society, a body composed of forty-two persons selected from among 
the most eminent cultivators of science, and which is entrusted with the 
distribution of an annual sum of £1000, placed by Parliament at the disposal 
of the Royal Society at the suggestion of Lord John Russell, in aid of 
scientific inquiries. One of the rules of that Commiitee is, that no sum 
whatever shall be given to defray the merely personal expenses of the 
experimenters ; all is spent on materials and the construction or purchase of 
instruments, except in a very few and rare instances in which travelling ex- 
penses form the essential feature of the outlay. A list of the objects to which 
the grants are devoted has been published by Parliament; among them are 
interesting investigations into the laws of heat, the strength of materials used 
in building, the best form of boilers, from the bursting of which so many 
fatal accidents are continually occurring, the electric conductivity of metals, 
so important for telegraphic communication, and into many other questions, 
in the solution of which the public generally have the deepest interest. The 
cost of these researches has been defrayed by these valuable grants. They 
have provided also for the construction of better and standard meteorological 
and magnetical instruments, for the execution of valuable drawings of scarce 
fossils and zoological specimens collected with great labour by distinguished 
naturalists, for the reduction and publication of astronomical observations by 
some of our most highly esteemed Astronomers, and for physiological re- 
searches which have an important bearing on our knowiedge of the human 
frame. Time indeed would fail me were I to attempt to describe all the good 
done and perhaps evil prevented by the distribution of these grants; and 
yet no portion of the money can be said to be really received by those to 
whom it is appropriated, inasmuch as it is all spent in the various means and 
appliances of research; in short, to quote from a letter addressed to the 
Secretary of the Treasury, at a time when the grant was temporarily withheld, 
“by the aid of this contribution, the Government has, in fact, obtained for 
the advancement of science and the national character, the personal and 
gratuitous services of men of first-rate eminence, which, without this 
comparatively small assistance, would not have been so applied.” I think 
that we were justified in terming this assistance small; for it is really so 
in comparison with the amount of other sums which are applied to analogous 
objects, but without that wholesome control of intelligent distributors, 
thoroughly and intimately conversant with the characters and competency of 
those who apply for the grants. The recognition of such a Board as has 
been sketched out by the Council of the Royal Society, may not lead to 
a greater expenditure of public money, indeed it is much more likely to 
curtail it; as some who now apply for aid through the interest of persons 
having influence with those in authority, who are generally but ill-informed 
on the subject-matter of the application, would hesitate long before they 
e2 


[xvill REPORT—1860. 


made a similar request to those who are thoroughly conversant with it; and it 
is on this account that comparatively few of the applications to the Govern- 
ment Grant Committee are rejected. Moreover, inasmuch as every grant 
passed by the proposed Board would afterwards receive the jealous scrutiny 
of Parliament, whose sanction must of course be obtained, I am disposed to 
think that were I to support the establishment of such a scientifie Council, or 
the formal recognition by the State of some existing scientific body in that 
capacity, I should be advocating that which would prove a valuable addition 
to the Institutions of my country. 

Before I finally conclude my observations on the important question I 
have introduced to your notice, and on which perhaps I have already said 
too much at the risk of wearying you, I must guard myself against one 
misapprehension, and that is, that we are anxious to obtain a large augmenta- 
tion of the £1000 now voted by Parliament. This is by no means our wish ; 
that annual sum is in ordinary years sufficient, and sometimes more than 
sufficient, and there is nothing that would be more deprecated than any 
large increase; but there is a very general feeling among those most 
competent to form an opinion on these matters, that when the well-con- 
sidered interests of science and the national good demand an extraordinary 
outlay, such as cannot be defrayed out of the proceeds of the ordinary yearly 
grant,—as, for example, for surveying and exploring expeditions, for the 
establishment and maintenanee of magnetic observatories, for the purchase 
of costly astronomical instruments, for expensive astronomical excursions, 
such as that to Teneriffe,—that the expediency of the grant is more likely to 
be properly investigated and tested, if referred to those whose avocations have 
given them the requisite knowledge, than if the concession or rejection of the 
proposal be permitted to depend on such accidents, as, whether this or that 
individual apply, or this or that statesman fill the office of Chancellor of the 
Exchequer. 

I trust that I may be pardoned the long digression in which I have 
indulged, in consideration of the importance of the subject. 

Having detailed some of the valuable services of our amateur Astronomers, 
let me not be accused of being unjust to the professional contributors to the 
data of that noble science. Most valuable Star Catalogues have resulted from 
the labours of our public Observatories, and from Greenwich in particular. 
There are also two Observatories which have, as it were, a quasi public 
character, viz. the Radcliffe Observatory and that of Armagh, which have 
contributed much to this department of Astronomy. Your former President, 
the accomplished and learned Dr. Robinson of Armagh, has lately presented 
to the astronomical world a Catalogue of the places of more than 5000 stars, 
and in so doing has conferred a most important benefit on his favourite 
science. 

But it would be an unpardonable omission were I to neglect to express our 
gratitude to our great National Institution at Greenwich, for the manner in 


ADDRESS. xix 


which it has consistently discharged the task imposed upon it by its founder 
and those who inaugurated its first proceedings. The duty assigned to it 
was “to rectify the tables of the motions of the heavens and the places of 
the fixed stars, in order to find out the so much desired longitude at sea, for 
perfecting the art of navigation ;” and gloriously has it executed its task. 
For two centuries it has been at work, endeavouring to give to the determi- 
nations of the places of the principal fixed stars and of the heavenly bodies 
of our own solar system, and more especially of the Moon, the utmost degree 
of precision; and during the same period, the master minds of Europe have 
been engaged in perfecting the analytical theory, by which the many and 
most perplexing inequalities of the Moon’s motion must be accounted for 
and represented, before Tables can be constructed giving the place of our 
satellite with that accuracy that the modern state of science demands. 

The very important task of calculating such Tables has just been finished. 
Our able and accomplished Director of the National Observatory, Mr. Airy, 
had caused all the observations of the Moon made at Greenwich, from 1750 
to 1830, to be reduced upon one uniform system, employing constants 
derived from the best modern researches; and a distinguished Danish Pro- 
fessor, who had been for some time engaged in calculating new Tables of the 
Moon, availed himself of the data so furnished. Professor Hansen happily 
brought to his task all the accomplishments of a practised observer, and of 
one of the most able analysts of modern times, combined with the most 
determined industry and perseverance. In the completion of it he was 
liberally assisted by our Government, at a time when an unhappy war had 
deprived the Danish Government of the means of further aiding their Pro- 
fessor, and a great astronomical work had been suspended for want of £300, 
a sum which many do not hesitate to spend on the purchase of some useless 
luxury. Professor Hansen’s Tables are now finished and published. They 
agree admirably with the Greenwich Observations with which they have 
been compared, and the mode of their execution has been approved by those 
competent to express an opinion on such a subject. They have been 
rewarded also with the Gold Medal of the Astronomical Society, a distinction 
never lightly bestowed. 

In paying this tribute to the merit of Professor Hansen, I must not be 
understood as wishing to ignore, far less depreciate, that of three very emi- 
nent geometers—Plana, Lubbock, and Pontécoulant, who have devoted 
years of anxious and perhaps ill-requited labour to the investigation of the 
Lunar inequalities, but who have never yet embodied the results in the only 
form useful to Navigation, that of Tables. 

A curious controversy has lately arisen on the subject of the acceleration 
of the Moon's motion, which is now exciting great interest among mathe- 
maticians and physical astronomers. Professor Adams and M. Delaunay 
take one view of the question; MM. Plana, Pontécoulant, and Hansen the 

other. Mr. Airy, Mr. Main the President of theAstronomical Society, and 


lxx REPORT—1860. 


Sir John Lubbock support the conclusions at which Professor Adams has 
arrived. The question in dispute is strictly mathematical; and it is a very 
remarkable circumstance in the history of Astronomy, that such great names 
should be ranged on opposite sides, seeing that the point invalved is really 
no other than whether certain analytical operations have been conducted on 
right principles ; and it is a proof therefore, if any were wanting, of the extra- 
ordinary complexity and difficulty of these transcendental inquiries. The 
controversy is of the following nature :—The Moon’s motion round the Earth, 
which would be otherwise uniform, is disturbed by the Sun’s attraction ; any 
cause therefore which affects the amount of that attraction affects also the 
Moon’s motion: now, as the excentricity of the Earth’s orbit is gradually 
decreasing, the average distance of the Sun is slightly increasing every year, 
and his disturbing force becomes less; hence the Moon is brought nearer the 
Earth, but at the rate of lessthan one inch yearly ; her gravitation towards the 
Earth is greater, and her motion is proportionably accelerated. It is on the 
secular acceleration of the Moon’s mean motion, arising from this minute 
yearly approach, that the dispute has arisen ; so infinitesimally small are the 
quantities within the reach of modern analysis. Mr. Adams asserts that his 
predecessors have improperly omitted the consideration of the effect produced 
by the action of that part of the Sun’s disturbing force which acts in the 
direction of a tangent to the Moon’s orbit, and which increases the velocity ; 
his opponents deny that it is necessary to take this into account at all. Had 
not M. Delaunay, an able French analyst, by a perfectly independent pro- 
cess, confirmed the results of Professor Adams, we should have had the 
English and Continental Astronomers waging war on an algebraical question. 
On the other hand, however, the computations of the ancient Lunar Eclipses 
support the views of the Continent; but if Mr. Adams’s mathematics are 
correct, this only shows that there must be other causes in operation as yet 
undiscovered, which influence the result; and it is not at all unlikely that 
this most curious and interesting controversy will eventually lead to some 
important discovery in Physical Astronomy. 

You are aware that at the suggestion of Sir John Herschel an instrument 
was constructed for the Kew Observatory, to which the name of Photohelio- 
graph has been given, because it is adapted solely to the purpose of obtaining 
photographic representations of the appearances on the Sun’s disc. Many 
difficulties have been encountered in the use of this instrument, but by the 
zealous exertions of the late Mr. Welsh, Mr. Beckley, and Mr. De la Rue, 
they have been overcome. It is to the last-named gentleman, so distinguished 
for his successful prosecution of celestial photography, that the Royal Society 
have entrusted a grant of money to enable him to transport the Photohelio- 
graph to Spain, to observe the total eclipse of the Sun, which is now 
approaching, and great interest will attach to records of the phenomena of 
the eclipse thus obtained. 

In Chemistry I am informed that great activity has been displayed, espe- 


ADDRESS. lxx1 


cially in the organic department of the science. For several years past pro- 
cesses of substitution (or displacement of one element or organic group by 
another element or group more or less analogous) have been the main agents 
employed in investigation, and the results to which they have led have been 
truly wonderful ; enabling the chemist to group together separate compounds 
of comparatively simple constitution into others much more complex, and 
thus to imitate, up to a certain point, the phenomena which take place within 
the growing plant or animal. It is not indeed to be anticipated that the 
chemist should ever be able to produce by the operations of the laboratory 
the arrangement of the elements in the forms of the vegetable cell or the 
animal fibre; but he may hope to succeed in preparing some of the complex 
results of secretion or of chemical changes produced within the living 


organism,—changes, which furnish definite crystallizable compounds, such 
as the formiates and the acetates, and which he has actually obtained by 


operations independent of the plant or the animal. 

Hofmann, in pursuing the chemical investigation of the remarkable com- 
pound which he has termed Triethylphosphine, has obtained some very 
singular compound ammonias. Triethylphosphine is a body which takes fire 
spontaneously when its vapour is mixed with oxygen, at a temperature a little 
above that of the body. It may be regarded as ammonia in which an atom 
of phosphorus has taken the place of nitrogen, and in which the place of each 
of the three atoms of hydrogen in ammonia is supplied by ethyl, the peculiar 
hydrocarbon of ordinary alcohol. From this singular base Hofmann has 
succeeded in procuring other coupled bases, which though they do not cor- 
respond to any of the natural alkalies of the vegetable kingdom, such as 
morphia, quinia, or strychnia, yet throw some light upon the mode in which 
complex bodies more or less resembling them have been formed. 

The power which nitrogen possesses of forming a connecting link between 
the groups of substances of comparatively simple constitution, has been 
remarkably exemplified by the discovery of a new class of amide acids by 
Griess, in which he has pointed out a new method, which admits of very 
general application, of producing complex bodies related to the group of 
acids, in some measure analogous to the Poly-ammonias of Hofmann. 

Turning to the practical applications of Chemistry, we may refer to the 
beautiful dyes now extracted from aniline, an organic base formerly obtained 
as a chemical curiosity from the products of the distillation of coal-tar, but 
now manufactured by the hundred-weight in consequence of the extensive 
demand for the beautiful colours known as Mauve, Magenta, and Solferino, 
which are prepared by the action of oxidizing agents, such as bichromate of 
potash, corrosive sublimate, and iodide of mercury upon aniline. 

Nor has the Inorganic department of Chemistry been deprived of its due 
share of important advances. Schédnbein has continued his investigations 
upon ozone, and has added many new facts to our knowledge of this 
interesting substance; and Andrews and Tait, by their elaborate investigations, 


lxxii REPORT—-1860. 


have shown that ozone, whether admitted to be an allotropic modification of 
oxygen or not, is certainly much more dense than oxygen in its ordinary 
condition. 

In Metallurgy we may point to the investigations of Deville upon the 
platinum group of metals, which are especially worthy of remark on account 
of the practical manner in which he has turned to account the resources of 
the oxyhydrogen blowpipe, as an agent which must soon be very generally 
adopted for the finer description of metallurgic operations at high tempera- 
tures. By using lime as the material of his crucibles and as the support for 
the metals upon which he is operating, several very important practical 
advantages have been obtained. The material is sufficiently infusible to 
resist the intense heat employed ; it is a sufficiently bad conductor of heat 
to economize very perfectly the high temperature which is generated ; and 
it may be had sufficiently free from foreign admixture to prevent it from 
contaminating the metals upon which the operator is employed. 

The bearing of some recent geological discoveries on the great question 
of the high antiquity of Man was brought before your notice at your last 
Meeting at Aberdeen by Sir Charles Lyell in his opening address to the 
Geological Section. Since that time many lrench and English naturalists 
have visited the valley of the Somme in Picardy, and confirmed the opinion 
originally published by M. Boucher de Perthes in 1847, and afterwards con- 
firmed by Mr. Prestwich, Sir C. Lyell, and other geologists from personal 
examination of that region. It appears that the position of the rude flint- 
implements, which are unequivocally of human workmanship, is such, at | 
Abbeville and Amiens, as to show that they are as ancient as a great mass of 
gravel which fills the lower parts of the valley between those two cities, ex- 
tending above and below them. This gravel is an ancient fluviatile alluvium 
by no means confined to the lowest depressions (where extensive and deep 
peat-mosses now exist), but is sometimes also seen covering the slopes of the 
boundary hills of chalk at elevations of 80 or 100 feet above the level of the 
Somme. Changes therefore in the physical geography of the country, com- 
prising both the filling up with sediment and drift and the partial re-excava- 
tion of the valley, have happened since old river-beds were at some former { 
period the receptacles of the worked flints. The number of these last, already 
computed at above 1400 in an area of fourteen miles in length and half a_ 
mile in breadth, has afforded to a succession of visitors abundant opportunities 
of verifying the true geological position of the implements. 

The old alluvium, whether at higher or lower levels, consists not only of 
the coarse gravel with worked flints above mentioned, but also of superim- 
posed beds of sand and loam, in which are many freshwater and land shells, 
for the most part entire, and of species now living in the same part of France. 
With the shells are found bones of the Mammoth and an extinct Rhinoceros, 
R. tichorhinus, an extinct species of deer, and fossil remains of the Horse, Ox, 
and other animals. These are met with in the overlying beds, and sometimes 


ADDRESS. Ixxiii 


also in the gravel where the implements occur. At Menchecourt, in the sub- 
urbs of Abbeville, a nearly entire skeleton of the Siberian Rhinoceros is said 
to have been taken out about forty years ago, a fact affording an answer to the 
question often raised, as to whether the bones of the extinct mammalia could 
have been washed out of an older alluvium into a newer one, and so redepo- 
sited and mingled with the relics of human workmanship. Far-fetched as wag 
this hypothesis, I am informed that it would not, if granted, have seriously 
shaken the proof of the high antiquity of the human productions, for that 
proof is independent of organic evidence or fossil remains, and is based on 
_ physical data. As was stated to us last year by Sir C. Lyell, we should still 
have to allow time for great denudation of the chalk, and the removal from 
place to place, and the spreading out over the length and breadth of a large 
valley of heaps of chalk flints in beds from 10 to 15 feet in thickness, covered 
by loams and sands cf equal thickness, these last often tranquilly deposited, 
all of which operations would require the supposition of a great lapse of time. 
That the mammalian fauna preserved under such circumstances should be 
found to diverge from the type now established in the same region, is con- 
sistent with experience; but the fact of a foreign and extinct fauna was not 
needed to indicate the great age of the gravel containing the worked flints. 
Another independent proof of the age of the same gravel and its asso- 
ciated fossiliferous loam is derived from the large deposits of peat above 
alluded to in the valley of the Somme, which contain not only monuments 
of the Roman, but also those of an older Stone Period, usually called Celtic. 
Bones also of the Bear, of the species still inhabiting the Pyrenees, and of 
the Beaver, and many large stumps of trees, not yet well examined by bota- 
nists, are found in the same peat, the oldest portion of which belongs to 
times far beyond those of tradition; yet distinguished geologists are of opi- 
nion that the growth of all the vegetable matter, and even the original scoop- 
ing out of the hollows containing it, are events long posterior in date to the 
gravel with flint implements, nay, posterior even to the formation of the up- 
permost of the layers of loam with freshwater shells overlying the gravel. 
The exploration of caverns, both in the British Isles and other parts of 
Europe, has in the last few years been prosecuted with renewed ardour and 
success, although the theoretical explanation of many of the phenomena 
brought to light seems as yet to baffle the skill of the ablest geologists. 
Dr. Falconer has given us an account of the remains of several hundred 
Hippopotami obtained from one cavern near Palermo, in a locality where 
there is now no running water. The same paleontologist, aided by Col. 
Wood of Glamorganshire, has recently extracted from a single cave in the 
Gower peninsula of South Wales, a vast quantity of the antlers of a reindeer 
(perhaps of two species of reindeer), both allied to the living one. These 
fossils are most of them shed horns; and there have been already no less 
than 1100 of them dug out of the mud filling one cave. 
In the cave of Brixham in Devonshire, and in another near Palermo in 


Ixxiv REPORT—1860. 


Sicily, flint implements were observed by Dr. Falconer, associated in such a 
manner with the bones of extinct mammalia, as to lead him to infer that Man 
must have coexisted with several lost species of quadrupeds; and M. de Vibraye 
has also this spring called attention to analogous conclusions at which he 
has arrived, by studying the position of a human jaw with teeth, accom- 
panied by the remains of a mammoth, under the stalagmite of the Grotto 
d’Arcis near Troyes in France. 

In the recent progress of Physiology, I am informed that the feature per- 
haps most deserving of note on this occasion is the more extended and suc- 
cessful application of Chemistry, Physics, and the other collateral sciences 
to the study of the Animal and Vegetable Economy. In proof I refer to 
the great and steady advances which have, within the last few years, been 
made in the chemical history of Nutrition, the statics and dynamics of the 
blood, the investigation of the physical phenomena of the senses, and the 
electricity of nerves and muscles. Even the velocity of the nerve-force 
itself has been submitted to measurenient. Moreover, when it is now de- 
sired to apply the resources of Geometry or Analysis to the elucidation of 
the phenomena of life, or to obtain a mathematical expression of a physiolo- 
gical law, the first care of the investigator is to acquire precise experimental 
data on which to proceed, instead of setting out with vague assumptions and 
ending with a parade of misdirected skill, such as brought discredit on the 
school of the mathematical physicians of the Newtonian period. 

But I cannot take leave of this department of knowledge without likewise 
alluding to the progress made in scrutinizing the animal and vegetable 
structure by means of the microscope—more particularly the intimate or- 
ganization of the brain, spinal cord, and organs of the senses; also to the 
extension, through means of well-directed experiment, of our knowledge of 
the functions of the nervous system, the course followed by sensorial im- 
pressions and motorial excitement in the spinal cord, and the influence 
exerted by or through the nervous centres on the movements of the heart, 
blood-vessels and viscera, and on the activity of the secreting organs ;— 
subjects of inquiry, which, it may be observed, are closely related to the 
question of the organic mechanism whereby our corporeal frame is influ- 
enced by various mental conditions. 

And now, in conclusion, I may perhaps be permitted to express the hope 
that the examples I have given of some of the researches and discoveries 
which occupy the attention of the cultivators of science, may have tended to 
illustrate the sublime nature, engrossing interest and paramount utility of 
such pursuits, from which their beneficial influence in promoting the intel- 
lectual progress and the happiness and well-being of mankind may well be 
inferred. But let us assume that to any of the classical writers of antiquity, 
sacred or profane, a sudden revelation had been made of all the wonders 
involved in Creation accessible to man; that to them had been disclosed not 
only what we now know, but what we are to know hereafter, in some future 


ADDRESS. Ixxv 


age of improved knowledge; would they not have delighted to celebrate the 
marvels of the Creator’s power? They would have described the secret 
forces by which the wandering orbs of light are retained in their destined 
paths; the boundless extent of the celestial spaces in which worlds on 
worlds are heaped; the wonderful mechanism by which light and heat are 
conveyed through distances which to mortal minds seem quite unfathom- 
able; the mysterious agency of electricity, destined at one time to awaken 
men’s minds to an awful sense of a present Providence, but in after-times 
to become a patient minister of man’s will, and convey his thoughts with 
the speed of light across the inhabited globe; the beauties and prodigies 
of contrivance which the animal and vegetable world display, from man- 
kind downwards to the lowest zoophyte, from the stately oak of the pri- 
meval forest to the humblest plant which the microscope unfolds to view; 
the history of every stone on the mountain brow, of every gay-coloured 
insect which flutters in the sun-heam ;—all would have been described, and 
all which the discoveries of our more fortunate posterity will in due time 
disclose, and in language such as none but they could command. It is re- 
served for future ages to sing such a glorious hymn to the Creator’s praise. 
But is there not enough now seen and heard to make indifference to the 
wonders around us a deep reproach, nay, almost acrime? If we have neither 
leisure nor inclination to track the course of the planet and comet through 
boundless space ; to follow the wanderings of the subtle fluid in the galvanic 
coil or the nicely poised magnet; to read the world’s history written on her 
ancient rocks, the sepulchres of stony relics of ages long gone past, to analyse 
with curious eye the wonderful combinations of the primitive elements and 
the secret mysteries of form and being in animal and plant; discovering 
everywhere connecting links and startling analogies and proofs of adaptation 
of means to ends ;—all tending to charm the senses, to teach, to reclaim a 
being, who seems but a creeping worm in the presence of this great Creation 
—What, I repeat, if we will not or cannot do these things, or any of these 
things, is that any reason why these speaking marvels should be to us almost 
as though they were not? Marvels indeed they are, but they are also myste- 
ries, the unravelling of some of which tasks to the utmost the highest order 
of human intelligence. Let us ever apply ourselves seriously to the task, 
feeling assured that the more we thus exercise, and by exercising improve 
our intellectual faculties, the more worthy shall we be, the better shall we 
be fitted to come nearer to our God. 


O8S Tetdalige) fardeiich svat WA or Aine ae: mye 


; . : : , ~ os ioe? a 

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Sar Wa cit ye set “Ph haat Va rth . i te ce Ep el? guids 
SOLAS. ) ‘ big ‘ : ‘ 7 is 

@ perc ley Pan Rid Sasa - yup Ai : : (le of aati ¥i any. 
b , j 1 


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4 
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at. a » CAI a vbiwaper Baw rie , v ‘alileoehs deta 
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Ssiy OT Fea Run ed erin cp 2 rl yj ix Anica 
Shadi ay ears to is wore sali 

Wie Qadivoetly Gd ies! pe Ha —prue ive : 
etd sizhe ei ile Hides: Saar emi Vinee ote 
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‘ nda eoeg eywojast ¥ aay f uh? Agoryt ical da Agta fl ea 


ay) i shire ha adear os ivesd ie * vet BS 


deciti nay org it toes f heonida sae cnet : no 


wl 
itt 130s) Morpers linda 29A 0 it WF sae 5 
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PRE HO Doditye. 7 eet a eae a? ha Oy) Pola S rio: ee 
PAY Bibs Gs 7) OFT} rest Sual gt. Vs + viyt ; i > drcHoleeyye 
fae bay eb iesgayl $ pil ME aff) BO ere! cd 9 ivttea ni ate 
SO ORS ave feck tartmet Phenin vr (ed ben. acivete wars W285 


“HAMA baisloo iz et ane @dife nts bnew «dtl ee 
Nh RET ot ge5t PERRO e! hte. ceed yOd gers lirtae. H ace ie 
tat Sodinar > trv it: 16 Chappe nh Yas $y Paid 
2 ee dene te yrs aioe at} sed) Ob: 2twork-e Gad Bir an 
Sppheals My of of DE 4 vhertéast paras art ele g| fay FE a 
SEW Tat Oe eet Soe a Gott Seige? ewe: =f scree werent 
Birt Mdilyid ont: coors SH ee alebgidyNercains ke anit 
eel at at hsdiit i Dee riqg im “sor ale tok ‘monwyithstet 
Src yeesrs yd biw ele wor ar wrnaess34) tai Det 
aw ligt. Bits al go tide iatiow. brivar Sadi tise), oc 

: = . per WO swe whanipu am 
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a > ~m, 
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im ©. a > ’ i 
¢ eo Aes re Pans er Tg thx dhksi ha by ARS 
> " » La) ee enka ee . 24 ‘ 
5. ae Of O& “m3 5 MSs cdpesai 
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’ haps PEO af m at Wile Fe 
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1, _ Fs 
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' 2 ae ok - 


REPORTS 


ON 


THE STATE OF SCIENCE. 


Report on Observations of Luminous Meteors, 1859-60. By a Com- 
mittee, consisting of JaMes GuatisHER, Esq., F.R.S., F.RA.S., 
Secretary to the British Meteorological Society, &c.; J. H. Guav- 
sTONE, Esq., Ph.D., F.R.S. &c.; R. P. Gree, Esq., F.G.S. &c. ; 
and K. J. Lowe, Esq., F.R.A.S., M.B.M.S. &c. 


In presenting a continuation of the Reports on the Observation of Luminous 
Meteors, it will be seen that the work is now placed in the hands of a Com- 
mittee, and it is with sincere regret that in presenting their first report, 
they have to announce the loss of Professor Powell, who died on the 11th 
of June, 1860. The preceding twelve reports were carried on solely by 
Professor Powell, but from the further prosecution of this labour he felt 
compelled to retire some little time since on account of failing health, having 
made arrangements for the continuation of the reports. Within the past 
year there does not seem to have been any unusual exhibition of meteors, 
either in August or in November; and there is little to be added to the ob- 
servations themselves ; in one instance only was the same meteor seen by two 
different persons, viz. that observed at Wrottesley Observatory and at Baldoyle 
(county Dublin), on March 10, 1860: this meteor was remarkable for its 
form and for its variation in colour, as noticed by both observers. It is much 
to be regretted that the observations of this meteor yet collected are insuf- 
ficient to trace its path, velocity, &e.; it is scarcely possible that so re- 
markable a meteor, visible from points so distant, can have passed unnoticed, 
and it is very desirable that if any observations may have been taken of it, 
that they should be forwarded to the Committee, for the purpose of being 
submitted to calculation. 

M. Julius Schmidt, now of the Royal Athens Observatory, in a communi- 
cation to M. W. Haidinger of Vienna, read by the latter at Vienna the 6th 
of October, 1859, before the Imperial Academy, has made some valuable 
observations upon some phenomena relative to the luminous tails of meteors, 
of which a résumé is given in the Appendix. An interesting paper has 
appeared in the Philosophical Magazine, April 1860, “On Luminosity of 
Meteors from Solar Reflexion,” by R. P. Greg, Esq. ; a brief analysis is given 
in the Appendix. In the Journal of the Franklin Institute there is a very 
interesting account of a large meteor seen over a large extent of country by 
daylight, on November 15, 1859; an abstract of this paper also appears in the 
Appendix. os 

1860. fs B 


Oct. 


Oct. 


Oct. 


Oct. 


Oct. 


REPORT—1860. 


Appearance and 


Brightness 
and Colour. 


Magnitude. 


erent eee ee ee eeee 


.|Globe form, twice the 
size of Ist mag. x 


star, as a spark. 


15 


21 


21 


22 


23 


=2nd mag. * 


Equal to 2nd mag. 


teeter nee 


6 30 p.m.|= Ist mag. x 


211 


a.m. 


Larger than 


p-m. 


of a lst mag, star. 
Planetary m ap- 
pearance. 


Three times the size| Orange, 


Velocity or — 


F 


Train or Sparks. Duration’ 


Peer ee ten enn eee e ee ennee 


Leaving a streak............ 


No streak or 
sparks. 
Slight streak 


separate 


Tne eee eee emma tenner en neee 


A streak composed of se-|Duration 0:3 sec. 


= to 2nd mag*...... =tolstmag.x,!Leaving a small mass of|Rapid. 


orange. 


and 
three times 


path, 


parate stars. 


Duratie 


separate stars in its| O:l sec. 


track. 


teen e eee teneenees 


Lasting 2 or 3 se 


No sparks .......... severe |Slow. Duratio 
2 seconds, { 


Direction or Altitude. 


om near # Pegasi, passing 
through y Aquarii to about 
3 Capricorni. 

om y Aquarii to 3 Capricorni 


Much 


red downwards from below 
Aquarius. 


oved from under « Ursee Ma- 
joris, from the direction of 
y Urs Majoris and fading 
away 2° beyond » Urs Ma- 
joris, having passed within 
30! of this star. 
oving horizontally from E. 
W. and crossing over 
2 Urse Majoris. 


ssed between Cassiopeia and 
the Pole Star, going towards 
-E. Its course was a line 


from  Cephei to E group of} 


Camelopardus, 


Rete teen een ewenenees Reser reeeeeeeee 


om the direction of Capella, 
starting at No. 36 Aurige, 


and fading away midway be- 
ween 9 Urs Majoris and 


Many 


No. 26 in the Lynx in a space 
devoid of stars. 


General remarks. 


in 
W.S.W. 


Moving on a slight 


curve, 


The meteors to- 


night gave a 
point of diver- 
gence in Cassio- 
ela, 


peia. 
Increased in bril-| 


liancy and disap- 
pearing at maxi- 
mum brightness. 
Much cloud. 
Aurora Borealis. 


Very bright for its! 


size. During the 
evening Aurora 


Borealis and 
lightning. 
At Highfield House 


at the time there 
was Aurora Bo- 
realis, lightning 


and snow. 


Lightning and 
snow. 


A singular meteor.|Ibid 


cloud and 
strong lightning 
i W.~ and 


A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS, 3 


Place, 


Highfield House. 


ener e neta enee 
eee eeneneerene 


One eaten eeeees 


Diss, Norfolk ... 


meteors.| Highfield House. 


Peete e eens 


Correspondent... 


Reference, 


Mr, Lowe’s MS. 


Tide “10 cil 


Thid. 


Ibid. 


A) Coccusnnacan Tbid. 


4 REPORT—1860. 
Appearance and Brightness : Velocity or ' 
Date. Hour Magnitude. and Colour. Train or Sparks. Duration. 
1859. |h m 3s 
Oct, 23) 8 1 p.m.|As a spark ............ Small S22. No sparks left............... Very rapid ; almo: 
instantaneously 
Oct. 23) 8 32 p.m.|= 2nd mag. «.........\Colourless .../No streak or train ......... Rapid. 
O-2 sec. 
Oct. 2311 46 30 |= 2nd mag. *, star-|Bright blue...|A streak left in its track. Rapid. 
like. 0-2 sec. 
Oct. 25) 2 O am./= 2nd mag. *......... IBIMOSscc5 5.0052 Withia train - j.ciuess ase Rapid. 
0-2 sec. 
ING Vie 2 Bebw een: 7. cccccecselcotecetoatsesee| cocenacarecatereetlee oan td oat tits on gu ccatoca nse aee URE senha et areeeeel 
&8 p.m. 
Nov. 2/12 45 a.m./= Istmag.*, appear-|...........ccc0ec.[escocsscescsccsccenccesscesectes Rapid :...\....:09 
ed as a flash, 
Nov. 3) 2 3 am./= 3rd mag.*......... Colowrless™. |Sireak: oerscjiecevnetoeoee RApIC y easvers 
Nov. 3) 2 4 am.= 3rd mag.......... Colourless™:*:|Streak Vscc0c:essesesteveee Rapid ....... PP 
Noy. 13) 2 50 am.'= 2nd mag. «......... pene Fe SELCHK sb ss  sapeuersrtertane Very rapid ...... 
IN OMe S| 2219 AML Ds. veacaeeetanec ss: van Iprilbanta® 30). siissvceveramast aves canst Instantaneous... 
orange scar- 
let. 
BMS LIA svi v0 vasigta tent akd assur aft dprotecgh caxcefuaned eles sect oa op ¥apesetgadare See ai a 
till 3a.m. 
Noy. 15) 8 55 p.m.|= in sizetoY¥. Globe Blue, bright Without sparks or train/Slow. Duration 
meteor. till it burst, then broke) O-4 see. 
into two or three small 
fragments and disap- 
peared. 
NOW 20) 8 Op iis 5.cecceeacandtee tesco. eee eee ee Ree eee ae SEROPRORSEPEPRY foe cuteagnecssbacs: 
Dee. 5 5 2 p.m.Twice the size of 2...'Colourless ...|.........s..0se00- Bs ott eenieee ISIOW.....0c000000eail 
Dee. 5 6 30 pm. = aba heiress Colourless) °F 2\55..ssccseceees coe Pevstsetern sees Eo sowie cam 
Bec, 5 9 25 ipim.j— Usbanmp.eric.s.-s--|...coecceteeteee es leer Meus sathonc te  SEEROOO SEC | ero 4 


om 


A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 5 


Direction or Altitude. 


m / Andromede towards §. 


45°. 

above t Draconis to near’ 
7 Herculis coming from the 
direction of Polaris. 
assed 15' BH. of bothsand x 
Ursx Majoris crossing over 
the star 36 in the Lynx, 
moving over 20° of space 
perpendicularly down. 
erpendicularly down from 
near No. 25 Canes Venatici. 


N. about 20° below the Pole 
Star, 


ell down from under Polaris 
at an angle of 80°, and fading 
away as it reached the Milky 


ay. 
m the zenith 
6 Persei. 
erpendicularly down through 
Cassiopeia. 
above the N. horizon, seen 
through a cloud. 


Poe Pe CREP eee CES C USS eee eee reer er) 


ell down in N.W. from 20° 
above the horizon, disappear- 
ing 10° above the horizon. 


C Slight Aurora Bo- 
downwards at an angle of] realis and distant 


General remarks. 


lightning. 


Temperature 24°°5 
at 4 feet, 18°°0 
on the grass. 


Many large me- 


teors, chiefly in 
N.E 


towards; 


Appeared, disap-| 
peared, and re- 
appeared four 
times in rapid 
succession, but 
never moved its 
situation. 


Lightning in N. at! 
the time. 


12 meteors. Clouds! 
numerous all 


Place. 


Highfield House. 


Observatory, 
Beeston. 


evening and 
night, and this, 
added to a full 
moon, caused 
most of the me- 
teors to be invi- 
sible. Faint Au- 
rora Borealis. 

An auroral arch at 
the time. 


Majoris only, moving over 
5° of space. 
ell down in W. from the alti- 
tude of 45°. 
ell perpendicularly down in 
§.W. from the altitude of 


40°, moving over 5° o 
space. ~ 


Tbid 


E. J. Lowe 


Highfield House.\Id. ............44. 


Observer. Reference. 


Mr. Lowe’s MS. 


se SAO BEE ROSE Ibid. 


DOR Sie cece ttae ce Ibid. 


Capt. A. §. IL/Tbid. 


Lowe. 


spare hich board re Ibid. 


6 _ REPORT—1860. 
io } 
Appearance and Brightness 5 Velocit; 
Date. Te Magnitude. and Colour. Erain.or Bparks. or reed 
1859. | h m 
Dec, 7 7 Op.m. |Larger than Jupiter,|Reddish ...... Long streak .........06000- Very rapid. D 
star-like. tion 2 secs. 
Dec. 14) 9 20 pm. }=2nd mag. *......... Orange ...... Sparks: ...1 cc clbswaavvevenbae Rapid. Durati 
2 secs 
1860. 
ans 62! 8 Open: |= 2p dnt BiZ0 Fh... se: 00-|vecns ska hlaess vc) oss snck cans snn4ss chess Faleren tthe Mita eer Ni ieee 
Jan. 24} 9 28 p.m. |Increased rapidly un-|Blue............ Train of separate sparks.../Slow. Duration ! 
til four times the secs. 
apparent size of| 
Jupiter. 
Many POA Mron 9) Ol cccssndeccesicdshistcusss{ecctecsossoatontce| dpgosneusG’s phaiteheooscesaesteds|Glaaaineetacsicce tam 
10 p.m. 
Feb. 24] 7 40 p.m. |=Venus .....cscceceeeelecsseceeeceeteoees With Calla ssiecesceonecsvoc|eobynntass ie eneceree 
Mar. 2/10 40 p.m. |=four timessize of }|Bright ......... Long tail......s.ssesees Wiese BloWisvvssesccey ea va 
Mar. 10] 8 40 p.m. |= Venus............... Bright as Ve-|Moderate speed, trail oOff.........:.cccsseeeuene 
nus. Colour} sparks left in its track 
of Venus. for 3 seconds after the 
meteor had vanished. 
Mar. 14} 8 45 p.m./Six times size of Ju-|Very bright, Burst into fragments...... Moderate speed .. 
piter. almost like 
lightning in 
appearance. 
Red in co- 
lour. 
Mar. 21) 7 15 p.m. |= Venus............... IBTignter than... .cs0s.cesesscesdentesse cress SIOW..:casssontagi 4 
‘ Venus. 
Mar. 21| 7 40 p.m. |= Venus............... Brighter’ thant|s.....:.:.ocssessasaetendtaceses Slow... ..<cs..005 
Venus. 
April 1) 8 10 p.m. |=2nd mag. « ......... Yellow......... Sani tall Oe ciecsscnecenevns SIGW Senseo. eee d 
April 17/Between 10)............ssccsetesscceseecssenescecanseselenessecenavccensessensescectvesselssveessastcesseeeeesn 
} & 11 p.m. 
ne Observations of Luminous Meteors 
Di. 
Aug. 16,11 45 p.m. |Equaltothe sizeof Ju- Bluish white..{It was accompanied by a|Slow, but its dura- 
i piter, but very supe- train. tion was short, as 
rior to that planet it did not travel 
1858. in brightness. above 5° or 8°. — 
Aug. 8| 8 45p.m.|Very bright, and/Blue............ It left a faint yellow train|Moderate........... i 
about the size o of light in its path. 
Jupiter. 
Aug. 8) 9 15 p.m. |Small but bright...... 13} rier cones Left a train visible for|Very slow .,....+.. 
several seconds. 
Aug 8) 9 38 p.m. |Small, about size of/Moderately {No train ...............:0008. Rapid in its mo- 
Saturn. bright. tion; visible for 
about 0:5 second 
only. 


A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 


7 


ee Sd 


Direction or Altitude. 
| 
‘rom 45° above the E. horizon, 

moved down at an angle 
of 40°. 

‘yom the Dragon’s Head, fell 
down at an angle of 40° to- 

wards W. 

‘ell down from 12° above the 
horizon in'8. by E. 

‘rom the direction of Polaris, 
passing midway between 3 
and Leonis, crossing ¢ 
Leonis, and fading away 
near 43 Leonis. 


Feet eeeeenaee Preece eee e eee we nanos 


Great Bear. 
n §.W., falling towards W.; 
half-way to zenith when first 


seen. 

m 60° altitude W. by N., 
falling down towards W. at 
an angle of 75°. 


Dee teweeeeeeeee 


§., fell down a long distance 
towards W., and passing 


Annee twee meee ee ee ee neearaenee 


m » Aurigs to Venus, over 
which planets it crossed, and 
then immediately vanished. 


PERN e reenter a een eeeneeereeseeeee 


from various Observers. 


started 10° from the zenith, 
ete west of the Milky 


Jay. 


ell down N. from about 45°|It was very light at|Blackheath 


from the horizon ; disappear- 
ed about 5° from horizon. 


tarted from a point 10° below}........+ 
@ Aquile, taking a westerly 


ell perpendicularly from 25° 
above « Virginis to a little 
south of that star. 


General remarks. Place. Observer. Reference. 
bsagedeccntiteds tetas Observatory, (R. Porter ....../Mz. Lowe’s MS. 
Beeston. 
Snow showers...... Mbidse asstas esses E. J. Lowe... |Ibid. 
GalOscctssccsamessss = Dbitling§esdcsss. sc. Td, ~csaenss iitesis. Thid. 
Sear eR Ricton res Oke bids, “aatverssses(lGsr wavsceracests:|EDIGs 
Six meteors seen...|[bid.  .......s.005 TAS 3s astro seee-(Lbids 
se sEhdENOSADNEE.c5 econ 1 mile W. of |Miss OC. Drége...|Ibid. 
Beeston. 
SddedcunscgenacccstReant 1 mile N.E. of |Mrs. R. Felkin...|Ibid. 
Beeston. 
Hseriestanctacestutcases Observatory, |Mr. R. Porter Ibid. 
Beeston. (assistant obs.) 
After the fragments|Highfield House.|Capt. A. 8. H.Tbid. 
were thrown out, Lowe. 
the meteor still 
moved on of the’ 
same size and 
brightness for a 
short distance. 
Meesdenadsstodcaas tents Observatory, {Miss Lucy White/Ibid. 
Beeston. 
Similar to the last.) Ibid. ............ Mr. R. Porter Ibid 
(assistant obs. ) 
Increased in size at\[bid.  ...:..4.444- ra RT ‘bid. 
last. 
Severalmeteorsmo-|Ibid. ....... .....[E. J. Lowe ......|[bid. 
ving veryrapidly. 
A POREROPERICOCOOLT SOE Greenwich ......|Henry C. Cris-[MS. communica- 
wick. tion. 
pacar IMG etc estes const sa | DOIG 
the time, and the 
stars in the path 
of the meteor 
could not beseen. 
pierise cdi ris fetes DIGS, hatise canes Tdi.) tiesaicaghas ,..{Lbid. 
J JaaeanaGeioss sat ere tale pid gist .comsern| Ls sceeveceeerste.(Lbid. 


8 REPORT—1860. ' 


Appearance and Brightness : Velocit: 
Date. Hour Magnitude. and Colour. Train or Sparks. or Detaieonl 
1858, |b m | | | 

Aug. 8) 9 44 p.m. /Equal in size to a 4th Very bright.../It left a thin train visible Slow...............5 

mag. * for about 1 sec, 

Aug. 8 9 52 p.m. Rather larger than Remarkably {No train ..,.........:00000 Very rapid ......05 

Saturn. bright. 
Aug. 8} 9 55 p.m. \Sizeofa3rd mag.*... Very bright./A very bright train. visible SlOW. 1.1.60 «ian 
Blue. for 3 secs. after the; 1 
extinction of the nu- ‘i 
1859. | cleus. 
Aug. 26} 8 24 p.m. |Six times the size of/Much brighter ................ccssseeeeeeseeseleaseaeaesans vesveeoal 
a Lyre. than a Lyre.) 

Aug. 30/10 14 p.m. |As bright as Capella |.........:0scccseslscccssscesssecesseseensovenanses Visible for about 3 

or 4 secs, 

Aug. 31) 7 5S p.m. |... ceseeesceeeseneeeeeses [Brighterwiisan| 00 25, .ins.s.fncsaacewacareel toutes PEAR 
any star then) 
visible. 

Sept. 22)Between _|Many shooting stars |............scccseleccccsecccseseeeentensenrecsecees Saree 

sunset and 
11 p.m. 

Sept, 24 Evening ...|Many shooting stars |............5.0++- | a slelnoa evpacweniecael Cone ene eee [Fetes ot aieeee oa 

Sept. 2810 20 p.m. Larger than Jupiter |Blue........+++. NQMC... wpe nccdae ccs ensnecounleceyreeksset nema : 

hee ZB a. | sacs svn ay csnnvvesefcugasted|exonnundersefeaier|saonsnas alana tate an 

Cig, 28}| Tsay Sark | Baprangeeseasceoosaccnonec: Very. bright....|Sceai.saasces Tee eee Visible for several 

secs. 

Oct. 27) 9° 9° p.m-|As lavge\as’ Capella... :|. 050: sscsepesses|-ccavecsonecaesoeantaev snes steeuelomemeetets Porcini 

aero! 7 GG peal. «16, Scape caucpeeee od usg Roser eroanoasegte SE RACHA COLDS RIOTS IASB NGA: Very rapid .,..,.. 

Nov, 7/ 9 33 pm... .sesceeeeeseneeneerenees As, bright) Wey. cepsovasesccpsmstoeenia ends (eemeemeanene ee er 

Capella. 

Noy. 9} 5 30 am. About 2° long......... Colour of red-|No sparks were seen ...... Its greatest bril- 
hot iron; its liancy lasted fo 
illuminating 30 seconds, buti 
power very remained visibl 
great. for 10 minutes. 

Nove 10) 9°40! pail... .cceneurcunsaeceeress Faint yellow. .'They left a train, similar'...........s00.:0000 “ 

to a faint streak. 


A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS, 9 


————— 


Direction or Altitude. General remarks. Place. Observer. Reference, 
ell from a little KE. of the Great)... ieee eee! Blackheath ...... (Henry C. Cris--MS. communica- 
Bear constellation diagonally’ | wick, | tion, 


towards the N.W., disappear- 
ing about 20° above the hori- 


zon. 

m 30° above the due §8.\Just before disap-\Ibid................ 1G BOR sacee eenre Ae ‘Tbid. 
horizon ; it went by W. to! pearingbelowthe| 

the horizon. horizon I di- 


stinctly saw it) 
separate, giving, 
at the same time 


a report like that! 
; of a distant rifle.| 
rom 40° above the E.S.B. ho-)..........cceeseeeseeees pid sesacpenve sett IGM) appear ate Thid. 
rizon to §.E., disappearing 
25° above the horizon. 
ell perpendicularly from near)............cc.cecseeens Wrottesley Ob-)W. P. Wakelin. |Ibid. 
a Ophiuchi to within 15° of servatory. 
the horizon. 
ell from 10° above » Ursx/This meteor paled Ibid.......,........ ees Rate Sere Tbid. 
Majoris, between » and Z, to} twice, and at- 
within a degree or two of] tained its maxi- 
12 Canum Venaticorum. mum brightness 
just before its 
disappearance. 
rom near w Cassiopeiz Gia-|,..............cseeeceee| Tidserocabevccstet TC Eee eee Tbid, 
gonally towards a point north 
of « Persei. 
bout Pleiades, moving W. to)............c.ccccseees (Ballater ...,...,.| J. H. Gladstone. |Tbid. 
Ee lage. ae: id. eee Ibid. 
orthern hemisphere; it fell)... eee Fort William, {Myrs. J. H. Glad-|Ibid. 
from W. to E. through 25°, Scotland, stone, 
descending from an altitude 
of 35° to about 25°. 
few degrees 8. W. of y Pegasi./It attained itsmaxi-/Wrottesley Ob-|F. Morton, Tbid. 
mum _ brilliancy) servatory. 


immediately be- 


fore it disappear- 
ed. 
descended vertically from the}...............s000000- 1] ays beadgnsonabponee Ne eiasgeeapsosase Thid. 
constellation Draco to within 
10° or 15° of the horizon. 
iE, from about 35° or 25°)..........cssccesseees CL ere Rare W. P. Wakelin. |Tbid. 
altitude. 
om midway between the Con-|............sseeeeeeeees iQ OEE" waRHocECCONre F. Morton ,..... Tbid. 
stellation Lyra and Hercules, 
at an angle of 45° to S. 
rom near 6 Pegasi, at an anglel............ccssece eee DIG Ona thece saa: We Srepccpapencies Ibid, e 
of 45°, to within 10° of the 
§.W. horizon. 
bout the same altitude as the|As it paled it got\Ibid. ............ ‘The under-gar- MS. 
Pleiades, and some 8° to the) gradually shorter dener at Lord 
south, and wider; it at Wrottesley’s, 
last looked like a the times by 
faint cloud. | F. Morton. 
m Capella to irius......... They were three in;Manchester ...... G. V. Vernon, 
number, 


10 


h 
37 


Feb. 16 


Mar. 3 


Mar. 10 


|Mar. 10 


REA Final: emawecenesas cede daenoseag 


REPORT—1860. 


Appearance and 


eer Magnitude. 


m 

10 p.m.|Its brightness was 
equal to that of a 
* of the Ist mag. 


10 35 p.m.|2nd mag. 


9 30 p.m. 


9 20 p.m. 


eee ee eee eee CTO eee ere eee 


9 20 p.m./The appearance gave 
the impression of 
3 feet in length. Its 
form was strictly 
defined, the front 
portion being in 
shape like the head 
of a lily, with a 
petal-shaped _out- 
line. From this it 
diminished grace- 
fully to the tail, 
not in straight- 
sided lines, but in 
curves. The tail 
was the  small- 
est, and apparently 
the most concrete 
portion of the 
whole. 

9 32 pm.|A bar of light in 
length equal to 
moon’s diameter, 
its breadth 3th o 
its length. 


Same 


Scarlet, 


Brightness 
and Colour. 


colour 
as Rigel. 


Velocity or 


Train or Sparks. Duration. 


No apparent train Very rapid ......008 { 


errr reer ere rer ererrrrire rrr creer ere reer rr 


pea- 
green. 


and of a red- 
dish colour. 


Bright 

brightest 
moonlight. 
Colour di- 
stinct and 
varied, the 
head pearly 
white, the 
tail bright 
ruby, with 
reddish- 

brown extre- 
mity,and the 
middle por- 
tions mark- 
ed by bands 
of various 
shades of 
colour. 


At first its 
colour was 
pure white, 
and as bright 
as Sirius. 
In its full 
the colour 
changed to 
green, and 
afterwards to 
a deep glow- 
ing crimson. 


as 


The outer portion of the 
stream was composed of, 
bright scarlet scintilla- 
tions. 


Lasted 5 seconds,| 
slow. 


oe 


It left behind a train of/The whole time was) 
pale yellow light. 2 secs. 4 


A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 11 


Direction or Altitude. General remarks. Place. Observer. Reference. 
(t fell from near the zenith,|.................0cec00 Manchester ...... G. V. Vernon. 
passing, through Orion’s Belt, 
and disappeared when on a 
level with Rigel. 
assing nearly horizontally]...............:.cceee0s Hendon’ ......... Mr. W. Grubb. 
through Ursa Major. 
£ an elevation of about 600/After dropping per.'Sidmouth ...... T. H. 8. Pullen. 
feet its direction was 8.8.H.| pendicularly for 
a short distance 
it separated 
itself into about 
eighteen globu- 
lar masses of dif- 
ferent colours, 
some about 8 or 
10 inches in dia- 
meter, and the 
others from 1 to 
3 inches. 
t fell from an elevation of 60°|.........ccsecseeeeeeeee Osborne ......... J. R. Mann. 
and N.N.E., and disappeared 
in the N. E. at an elevation 


of about 10°. 
bout 50° in a N.E. direction.|After falling about|Coleraine. 
: 50°, it burst into 
a number  of| 
sparks, like a 
rocket. 


direction was that of a/About 30 secs. after|Baldoyle(county/J. P. Culverwell, Mr. Lowe's MS. 
Dublin). E 


line drawn from Orion’s Belt, 
through the Pleiades, and 
onward to the W. of Cassio- 
. disappearing in the 

partion of tp hemi- 
sphere. 


the disappearance 
of the meteor 
there was a low 
rumbling thun- 
der in the N.E., 
which continued 


sq. 


fully 2 mins. 


Vers ched tts MS. communica- 
tion, 


was seen at an altitude of 45°,|The stars for 15° Wrottesley Ob-J. H. 
on each side of 
its path were 
paled as by the 
presence of the 
full moon. 


and darted perpendicularly 
between the Pleiades and Al- 
gol to the horizon. 


servatory. 


12 REPORT—1860. 


a 


Velocity or 
Duration. 


Appearance and Brightness 
Magnitude.’ and Colour. 


Date. Hour. Train or Sparks. 


1860. |h m 
Mar. 10) 9 50 p.m./It appeared about/Very bright, at}...........csseeseseereeseeeeeees Visible for a secon 
2rds of the size of first purple- or two. 
the moon. red and 
then green, 
= Venus. 


DME |e Ol aeIM.| eacccesveusnesresseereres- Very brightiz.:| Aessseessat Winer coneesrsteavees 2 or 3 secs. sesevenns 


April 14) 9 4 pumi}.c.cesceeeeeeeesenseeseees Hiqual to VAI=| erica taevanvecsssnsssepecucen| sucnyeestshepa <x cneem re 
debaran in 
brightness. 


April 26] 7 52 p.M.)..ccccccscesscceeereereenes At first  bril-/It left a very luminous tail! It was visible about 
liant white,| behind it. a second. 

and = after- 
wards pur- 
ple-red. 


APPENDIX. 


No. 1.—In the Journal of the Franklin Institute, Philadelphia, February 
1860, is a collection of observations of a very remarkable meteor seen by 
daylight, on November 15, 1859, by Benjamin P. Marsh, Esq. 

This meteor made its appearance at about half-past 9 o’clock a.m. (New 
York time), the weather being perfectly clear, and the sun shining brightly. 

It was seen at Salem, Boston, and New Bedford, Massachusetts; Provi- 
dence, Rhode Island; New Haven, and many other places in Connecticut ; 
New York City; Paterson, Medford, and Tuckerton, New Jersey ; Dover, 
and other places in Delaware; Washington City ; Alexandria, Fredericks- 
burg, and Petersburg, Virginia. 

It was heard at Medford, New Jersey, and at all places in that State, south 
of a line joining Tuckerton and Bridgeton, and throughout nearly the whole 
of Delaware. : 

With perhaps two or three exceptions, it was not seen by any one in New 
Jersey, south of the Camden and Atlantic Railroad ; that is to say, through- 
out the very region where the report was loudest. 

Many persons there saw a momentary flash of light “like the reflexion of 
the sun from a looking-glass,” but could not tell where it came from. The 
appearance of the meteor as seen at many places is described, and the results 
from their discussion are as follows :— : 

1. The inclination of the meteor’s point to the vertical was probably about | 
35°, and the direction of its motion nearly west. The observations at Med- 
ford and Petersburg indicate a much more southerly movement, but those of . 
Washington, Alexandria, and Dover, require it to have been almost due west. | 

2. The column of smoke was near 1000 feet in diameter, and its base was 


A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 13 


Direction or Altitude. General remarks. Place. Observer. Reference, 
Tt fell at an inclination of N.W.|It travelled about Bradford......... M. D. 
to W. 15° and then W. W. M. 
burst ; it appear- E. M. C. 
ed at first as J.C. 
though the moon Cc. W. 
had fallen to the 
earth. 
BING SO 5 ccosssccesssvctesoes It appeared sta-/Torquay ......... FR. Vivian. 
tionary, but in- 
creased in bright- 
ness for 2 or 3 
seconds, when it 
suddenly disap- 
peared. 
¢ darted from a point half-Its path was con-|Wrottesley Ob-|J. H. ............ MS. communica- 
way between the Pleiades} cave to the hori-| servatory. tion. 
and @ Persei to a point about} zon. 
one-third of the distance 
from Aldebaran to « Aurige. 
t fell from the zenith to the)......, eis depanySieeeaey op Manchester ...... G. V. Vernon. 


vertical about four miles north of Dennisville, at a height of near eight miles, 
which may be assumed to be the approximate position of one point in the 
meteor’s path. The height is inferred not merely from the angular elevations 
of the smoke as seen from different points, but from the interval between the 
flash and the report, as observed at Beasley’s Point. This position assigned 
to the base of the cloud, from local reports, coincides pretty nearly with that 
indicated by distant observations. 

At New Haven, latitude 40° 18’ 18", longitude 72° 55! 10", at an eleva- 
tion of 6°, the bearing was S. 35° 34! W.; and at Alexandria, latitude 38° 49', 
longitude 77° 4', at an elevation of 102°, it was N.763° E. These directions 
meet half'a mile west of Dennisville in latitude 39° 112/, longitude 74° 502/; 
the line from New Haven having a vertical height at this point of 292 
miles, and that from Alexandria 243 miles. Continuing the path, as ob- 
served at Alexandria, down to 94° elevation, we have corresponding azimuth 
764°, and the lines then meet half a mile north-west of Dennisville at a 
height of 225 miles; but this makes the nearest point in the meteor’s path 
twenty-four miles from Beasley’s Point, and consequently the interval there 
between the flash and the report two minutes instead of one, as observed. 
Besides, the observations on the smoke show pretty clearly that the minimum 
height at Dennisville could not have exceeded ten miles. We must there- 
fore conclude the meteor’s actual position to have been several miles east of 
that indicated by these distant observations. 

3. On the above supposition, the meteor’s path would reach the earth near 
Hughesville, on the north-western boundary of Cape May County, in which 
Vicinity, or perhaps still further west, it is probable that the meteor or some 
of its fragments will yet be found. 

4. Some observers must have seen the meteor at a height of more than 


14 REPORT—1860. 


100 miles; and, to have completed its path within their estimates of time, it 
must have had a velocity of from thirty to fifty miles per second. 

The extreme shortness of the time occupied in its flight, is proved not 
merely by the estimates of several observers, but by the failure of people in 
the vicinity of the explosion to distinguish the source of the sudden flash of 
light seen by them, and by the impression of even the most distant observers 
that it fell very near them. 

5. The sound was explosive, and moé caused by the falling in of the air 
after the meteor. In the latter case it must have been continuous and un- 
interrupted, but the testimony of Dr. Beasley and others shows that it ceased 
entirely and then began again. 

Supposing the meteor to have been a stony mass, we may, perhaps, con- 
sider the explosion to have consisted of a series of decrepitations caused by 
the sudden expansion of the surface, the whole time of flight not being suffi- 
cient to allow the heat to penetrate the mass. At the forward end these ex- 
plosions would take place under great pressure, which may account for the 
loudness of the sound. 

6. The estimated duration of the sound at Beasley’s Point was not less 
than one minute, indicating that the most distant point of the explosion was 
not less than twelve miles further from that place than its nearest point. 
Comparing this with the position of the assumed path, we find that, during 
the explosion, the meteor must have travelled fifteen or twenty miles, occu- 
pying about a second of time. 

7. The explosions were very numerous, arranged in two series, the whole 
occupying only half a second of time, but the individual sounds were distin- 
guishable, because of the different distances they had to travel to reach the 
ear. The velocity of the meteor being more than 100 times that of sound, 
the reports must have come in the order of distance and zoé in the order of 
their occurrence, causing the end of the explosion to be heard before the 
beginning. The faint rushing sounds first heard by Mr. Ashmead must 
have had their origin below the explosion, and been caused by the flight of 
the fragments towards the earth. If the direction of the first faint sound 
could be indicated by persons further west, it might serve to point to the 
place where the fragments fell. 

8. The meteor lost its luminosity with the explosion or shortly after, and 
hence was not seen by persons in Cape May County and vicinity, it being 
too much overhead to come within the ordinary range of vision, and the time 
of flight being too short to allow them to direct their eyes to it after seeing 
the flash. 

If the heat be due to the resistance of the air, it must be principally deve- 
loped at the surface of the forward half of the meteor. Consequently 
most of the explosions must occur then, and the force of each be directed 
backward, tending to check the velocity of the mass. In fact, we may per- 
haps consider the series of explosions to be merely one of the forms of the 
atmospheric resistance. This must increase rapidly with the density, although 
it may be insufficient to account for so great a reduction of speed as would 
entirely destroy the luminosity of the meteor before it reached the earth. 

9. Irom the tremendous force of the explosion, and from the fact that this 
meteor was seen by persons who were not within 200 miles of any part of 
its path, as at Salem, Massachusetts, and Petersburg, Virginia, we must cer- 
tainly conclude that it was of very considerable size; but we seem to have 
no data for any approximation to its actual dimensions. It was certainly 
heated to a most intense brightness; and the experiments of Professor 
J. Lawrence Smith, detailed in Silliman’s Journal, vol. xix. fol. 340, second 


a. te 


A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 15 


series, in which he found that a piece of lime, less than half an inch in dia- 
meter, in the flame of the oxyhydrogen blowpipe, had, when viewed in a clear 
evening, at the distance of half a mile, an apparent diameter twice that of the 
full moon, show conclusively that no reliance can be placed upon calculations 
founded upon the apparent diameter ef bodies in a state of incandescence. 

10. The apparent form of the meteor, that of a cone moving base fore- 
most, may have been due to its great angular velocity, combined with the 
effect of irradiation above referred to. ‘The impression made upon the eye 
by the incandescent body itself, would doubtless be greater than that made 
by the sphere of light surrounding it. Consequently we should continue to 
see the body itself after the impression of the mere glare had faded awav ; 
so that the apparent diameter of the end of the tail may represent the actual 
angular diameter of the body. 

11. The invisibility of the meteor to persons at Philadelphia and vicinity, 
was no doubt due to the position of the sun, the direction of which then 
coincided with that of the meteor. 


No. 2.—Abstract of a paper by R. P. Greg, Esq., F.G.S., in the Philoso- 
phical Magazine, April 1860, “On Luminosity of Meteors from Solar Re- 
Hexion.” 

With reference to the cause of the luminosity of shooting stars, the author 
proposes to prove that their luminosity cannot arise from solar reflexion, 
a theory partially supported by Sir J. Lubbock and others. He observes 
that the very sudden appearance and disappearance of shooting-stars and 
small meteors, and their general resemblance on a small scale to comets which 
shine by solar reflexion, certainly favour the idea, either that suddenly enter- 
ing the cone of the earth's shadow they are instantly eclipsed, or conversely, 
become visible as they emerge from it; or secondly, previously self-luminous 
in planetary space, they may become suddenly extinguished on entering the 
denser atmosphere of the earth; or thirdly, they may suddenly become visi- 
ble and luminous only on entering the earth’s atmosphere by friction and 
compression, by rapid absorption of oxygen and sudden chemical action, or 
by electrical excitation. 

The author then refers to Sir J. Lubbock’s paper in the Philosophical 
Magazine for February 1848, and shows by a different treatment how un- 
likely, if not impossible, it is that ordinary shooting-stars (those not show- 
ing symptoms of active ignition within the lower limits of the earth’s atmo- 
sphere) can ever shine by reflected solar light ; and this simply from the fact 
that they would be too far off for us to observe such small bodies, at even 
the minimum distance at which (at certain times and places on the earth’s 
surface when and where we know they are very frequently seen) they 
actually could be so visible; and concludes his paper by remarking that, if 
his calculations, &c. be correct, the majority of shooting-stars do not shine 
by reflected light. 


No. 3.—M. Schmidt on the Luminous Trains left by Meteors, &c. 

M. Schmidt repeats an observation of M. Faye’s in the ‘ Comptes Rendus,’ 
vol. xxxii. p. 667, relative to the small amount of moveability in the tails or 
luminous trains not unfrequently left by meteors, which seems to prove that 
the former must be found in the atmosphere belonging to and surrounding 
the earth, and not in the firmament which lies beyond it. M. Faye observed 
one of these tails through the telescope, and he saw it “lingering for more 
than three minutes, without changing its place very perceptibly.—Other 
observers have observed them to remain for more than seven minutes.” M. 


16 REPORT—1860. 


Schmidt remarks on the strangeness of this stationary condition of the lumi- 
nous trains of meteors, likewise on the cloud-like appearances generally left 
by detonating meteors even in the day-time, when we come to consider the 
enormous velocity of the meteors themselves through the higher regions of 
the atmosphere ; but he says, “ we must recollect an easy and interesting ex- 
periment, by which we may obtain a similar result. If you take a common 
lucifer match, still burning, or when it is just about to become extinguished, 
and throw it from you in any direction, either quickly or slowly, you will 
in many cases perceive, either a straight immoveable line, or an undulating 
or curling line of white-grey smoke, standing still in the air, if the air is calm 
and not in motion.” 

M. Schmidt observes how important observations, whether telescopic or 
otherwise, are respecting the tails of meteors,—I1st, as regards their proper 
motion; 2nd, the downward curvature sometimes exhibited by them, and 
the way in which they break up and disperse; and 3rd, the means they may 
afford of ascertaining by parallax their height above the earth, a matter of 
very great importance for ascertaining at what heights the atmosphere ceases 
to have any influence. 

M. Schmidt then proceeds to cite a number of instances from his own 
catalogue of meteors, where tails have been observed of long duration, or as 
offering very peculiar appearances: e. g. 

1664. Aug. 3. A very large meteor with curved tail, seen at Papa, Hun- 
gary. 

1791. Nov. 11. At Gottingen and Lilienthal, a meteor left an undulating 
tail of a shining white colour, in parts alternately showing the prismatic 
colours ; then became more curved, and turned into vapour of a pale yellow- 
ish colour before finally disappearing. 

1798. Oct. 9. Brandes witnessed at Gottingen how the tail of a bright 
shooting-star bent itself within 15 seconds like a bow. 

1840. July 30. Ditto at Vienna, in 15 seconds also. 

1845. Oct. 24. Schmidt observed at Bonn the change in the form of the 
tail of a meteor in 4 minutes; it became severed and bent, and dissolved 
into small grey clouds. The whole mass moved 1° from its original place at 
final disappearance. 

1852. Oct. 26. A large meteor seen in Pomerania, left behind it a spiral 
tail 3° long, which contracted soon into a ball, and again passed into a spiral 
curve, finally assuming the shape of a capital Z. 

1854. Aug. 1. At Gottingen, a fine meteor left behind a bright tail 3! 
wide and 2° in length, lasted 8 or 9 minutes after dividing itself into three 
oval balls, and showing at first uneven undulations or knots, while the tail itself 
shortened and became more likea W. Whilst these changes took place in the 
tail, the whole mist-like mass moved along the sky in a nearly opposite direc- 
tion to the motion of the fireball itself; the tail had thus moved 9° in 8 minutes. 

1859. Aug. 9, 10, 11. During these three nights, M. Schmidt at Athens 
succeeded in observing, on four different occasions, the curving of meteor- 
tails through the telescope. The whole time, in three cases of visibility, was 
170", 140", and 220" respectively ; in one case only 10" or 12". The curva- 
ture of the tail began to be perceptible almost directly after the meteor 
vanished, and the proper motion in one direction very decided. In one of 
these cases, viz. on Aug. 11, a bright orange-coloured shooting-star left a tail 
visible to the naked eye 4" or 5", but through the telescope 220"; the direc- 
tion about from E.N.E. to*W.S.W. The following figure shows the real mo- 
tion of the tail, compared with the apparent motion of the shooting-star. 

The tail finally broke up into a number of small fragments. 


| 


A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 17 


ab, the apparent motion of the shooting-star. 

a, tail at end of 5th second. 

(, tail at end of 12th second. 

y, tail at end of 180th second. 

6, tail at end of 220th second. 

A B, apparent motion of the tail nearly at right 
angles to a b. 


Aug. 9. Representing, after another meteor, a 
similar movement of tail as compared with 
the meteor itself. 


B 


M. Schmidt states that credible cases, where the tails of meteors and shoot- 
ing-stars remain visible lunger than 5 seconds, are very rare and isolated. He 
cites thirty-nine instances from his own catalogue, of which we select seven 
instances of longest duration. 


1751. May 26. 3" 30™"...... Kraschina (Agram meteoric iron fall). 

fea0g.Oct. 10. 1° «...ee On the high seas. 

1840. July 30. Lo én ee ae), Vieniias 

1847. Jan. 10. LOM sess.» Vienua. 

1847. Nov. 10. YO" ...... Benares. 

1853. Aug. 26. 107 eae oe Mazzow. 

1856. Oct. 29. 30™....2.. Laybach. 

Among the thirty-nine instances given by M. Schmidt, there were more 
than one instance of the tail winding or doubling itself up, nay, of even 
vanishing and then re-appearing. 


Duration of Meteors. 

M. Schmidt also offers further remarks on the duration of meteors, and he 
observes how rarely they are visible for more than 1 second; that 0! 2! to 
1’ 5" is the usual time of visibility ; the practised observer knows that the 
majority in fact of shooting-stars only shine during the fraction of a second. 

In all probability the short moment during which the light shines is at the 
same time the moment of its partial and final extinction. 

The time during which a shooting-star is visible is a subject for the art of 
more refined observation, and M. Schmidt hopes that much attention will be 
directed “towards determining the duration with regard to colours and any 
anomalous motions of meteors.” In his treatise on Meteors, p- 15, M. Schmidt 
states how long the tails or luminous trains of meteors remain visible, with 
regard to colour, viz. as follows:— 

sec. Mean error. 
With white meteors, the mean =1-00 in 24 observations.... 0°05 
With yellow meteors, the mean=1'51 in 18 observations.... 0°15 
With green meteors, the mean =1-96 in 12 observations.... 0°29 


| 1860. c 


18 REPORT—1860. 


On the other hand, at p. 50, the time during which tails are visible upon the 
whole number, with regard to these different colours :— 


sec. 

‘Time of duration for pe atte ay =0°85 in 64 observations. .p. 1849. 
Time of duration for ae cota =0'90 in 80 observations. a.p. 1849. 
ibm ot iumeaoe snd lceee oe to = 128 in 14 observations. a-p. 1849. 
"Time of duration. for ite le a =1:60 in 5 observations. a.p. 1849. 
aap tte tcehe Avesta ee =0-91 in 12 observations. a.p. 1849. 


Likewise in the year 1850 the longer duration of the coloured meteors 
showed itself in the following proportional means :— 


secs. 
Duration of the white =1-16 in 12 observations. 
Duration of the yellow =1'25 in 8 observations. 
Duration of the yellowish red=1°41 in 6 observations. 


If we consider the time during which the light of the meteor itself lasted 
without regard to any other phenomena, we find in his catalogue the follow- 
ing instances which show that in the case of many thousand observations 
it is very rare that a shooting-star or meteor remains visible for more than 5 
seconds. 


Date. Duration. Place of observation. 
secs. 
1783. August 18 s..ccocsss+scenteejn 6 GO, |Lendon. 
184.2. November 1.........e0.00.6-, LO | |Hamburg. 
1842. November 7......cecseeseeves} 10 | |Hamburg. 
1842. November 21 ......ssseeeeee $  |Hamburg. 
1843. September 19 .........ceeee 7 | |Hamburg. 
1843. September 22 ,,,...seceeeeee 9  |Hamburg. 
1844. August Lh ccsesssadsnare: cer 6 |Hamburg. 
1846. August TO ccssesssdesces ees 8 (Bonn. 
1847. November 29 ......seeserees 8  |Bonn. 
1851. September 26 ..........c000. 11 Minster. 
1659 November S$” \ i. .icessene. 0s 10 =‘ |Miinster. 
LOS; “August Is. .5,.scessauereses< 35 _ |G6ttingen. 
1854. December 8.......2.se0ceee00| 8 |Vienna. 
1656: October Zon cesssevenscees 12 |Laybach. 
1857. ? sda fectee to gee ne. Mae | Mere 
1859, July 27 ieecdsivsgeeesaceee] «12 Athens: for 967 are 


The following remarks on the hypothesis that the intensity of the light 
of the meteors is caused by the oxygen in the atmosphere, are here translated 
verbatim from M. Schmidt’s communication to M. Haidinger :— 

“In consequence of the observations which were then being made by Ben- 
zenberg, Brandes, Felder, Heiss, by myself and others, in the year 1851, I 
examined into this question more closely, and I arrived at a result which was 


* Mr. Greg found one account of this meteor stating it was 20”, seen in an are of 75°. 


om 


A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS, 19 


indirectly opposed to that hypothesis: since it is a difficult matter thoroughly 
to refute old objections, however untenable, I may perhaps be permitted here 
to refer to them, and to refer to numbers instead of to opinions. 

“ We all know that the intensity of the light of shooting-stars is estimated 
according to the brightness of the stars, and we therefore, e. g., say that a 
meteor is of the first magnitude when its light equals that of Arcturus or 
Vega. If it shines brighter than Jupiter or Venus, we designate it a small 
fireball. If we put such numerical values for the shooting-stars so as to 
express the intensity of their light, and if we call A the mean height of the 
shining portion of the luminous track above the surface of the earth, we 
obtain the following mean proportional values, which, in the year 1851, I 
deduced from the observations then made (see my work, p. 111) :— 


Meteor of Ist magnitude, k=16:2 geographical miles, for 14 observations, 
Meteor of 2nd magnitude, A=15:°9 geographical miles, for 20 observations, 
Meteor of 3rd magnitude, A=10°8 geographical miles, for 24 observations, 
Meteor of 4th magnitude, k= 8:5 geographical miles, for 21 observations, 


Hence, therefore, it follows that the large meteors belong to the highest 
regions of the earth, where, as we generally suppose, there exists scarcely any 
air at all; that, however, the small meteors which have a feeble light are seen 
nearest to the earth, and occupy the limits of the atmosphere, where the latter 
still exists in a greater and more perceptible degree, and that they descend 
still lower. It is therefore not the oxygen of the air which is in the main the 
chief cause and origin of the burning or glowing of the meteors.” 


Note by Mr. Greg.—That the smaller shooting-stars are frequently nearer 
than the larger meteors, may possibly be still further supposed to be true, 
from the fact that usually they are seen to move more rapidly than the larger 
ones. Still exceptions may exist, as in the case of very large, and probably 
aérolitic fireballs moving horizontally and parallel to the horizon. 

The height at which meteors are not merely luminous, but can leave nearly 
stationary trains of light, is truly surprising; one would almost have 
imagined, at that distance from the surface of the earth, some retardation in 
space of the attenuated and upper stratum of air, as compared with the rapid 
movement of the earth on its own axis. 

It is to be regretted that the extreme limits of the auroral regions are not 
yet more precisely ascertained ; but it is not improbable that shooting-stars 
are commonly visible, or luminous, precisely in that very region, and that 
their luminosity may to some extent be owing to electrical excitation. 


No. 4.—In the ‘Comptes Rendus,’ vol. xxxvii. p. 547, M. Coulvier-Gravier 
gives a list of 168 bolides observed from 1841 to 1853, classed as follows:— 


Istisizenas sa sevetectevess Bl 
Ind SiZG, ess evseenieestere OO 
Brdheigers, sore yesscaied octe _98 


168 


of which latter, viz. those of the 3rd size, he states as being larger or brighter 
than Jupiter or Sirius; the relative or absolute size of the two other classes are 
notstated. These three classes described average arcs or paths as follows :— 


(1) 31... are of 42° 4! 

(2) 39... are of 26° 7! 

(3) 98 ... are of 22° 7 
c2 


20 REPORT—1860. 


Their directions at different hours of the night, and numbers, are given in 
the annexed Table :— 


6pe.m.to10p.m.|10P.m. to 2 a.m.| 2 4.m. to 6 A.M. 


Directions. Number. Number. Number. Totals 
N. 2 Ze Hae 4 
N.N.E. 2 A 2 4. 
N.E. 3 4 1 8 
E.N.E. . 1 5 y 8 
E. 1 Us 2 10 
E.S.E. 8 8 1 qs7 
S.E. 4 8 1 13 
S.S.E. A 9 5) 16 
8. 4. as 3 £4 
S.S.W. ] 4. 5 10 
S.W. oe 8 5 13 
W.S.W. 3 5 1 9 
Ww. 1 3 g 6 
W.N.W. 6 9 8 93 
N.W. 4 4 6 14 
6 


a ee 


The 44 bolides which were observed froin 6 p.m. till 10 p.mM., were seen 
during 6943 hours of observation, which gives one bolide for 15 hours 
47 minutes for that part of the night, of which the average is 9 o'clock. 

The 76 bolides from 10 p.m. till 2 A.M. were seen in 8483 hours of obser- 
vation, which gives one bolide for every 11 hours and 10 minutes for the 
second part of the night, with the mean of midnight. 

The 48 bolides from 2 A.M. till 6 A.M. were observed in 340 hours, which 
gives one bolide for every 7 hours and 5 minutes for the third part of the 
night, the mean being 3 A.M. 

The number of bolides being therefore inverse of the times as above, for 
each bolide, if one allows 100 for midnight, we should find from 


No. of bolides, 
6 10 10, average 9 P.M. ...... = 71 
10 to ¥, average midnight ... =100 
2to 6, average 3 A.M. ...... =158 


The number of bolides seen about 6 A.M. is triple the number of bolides 
observed in the evening, a result which accords with the horary and usual 
variations of shooting-stars generally. 

Out of 168 bolides observed, there were 101 which left longer and shorter 
trains of light of different degrees of duration. 

Out of the same number there were 20 which burst into sparks after a 
course more or less arrested by the rupture. 

Lastly, there were 8 which changed their original velocity, or became sta- 
tionary in their course; two which changed their direction towards the end 
of their path, and ove which had an oscillatory movement. 

M. Coulvier-Gravier elsewhere remarks that 6th magnitude falling stars 
have arcs or paths of from 40° to 9°. 


ca 


A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 21 


In the ‘ Comptes Rendus,’ vol. xlv. for 1857, p. 257, M. Coulvier-Gravier 
remarks, in a series of observations on the August periodical meteors during 
a period of twelve years, that the maximum number per hour, from 9 P.M. to 
10 p.M., are seen between the N.E. and E.N.E. to 2° 5! of N.E. From 2 to 
3 A.M. between E.S.E. and S.E., 3° of E.S.E. From 9 p.m. to 3 A.M. the 
maximum has advanced 65° towards the South (or 11° per hour); so that 
one would conclude that at 6 a.m. the maximum would be between the S, 
and S.S.E., 7° of S.S.E. 

The above is also confirmed by the general result for other months of the 
year, 7. e. the maximum for August being in the morning between the S. and 
S.S.E., the general average for the year, of shooting-stars, being E.S.E. 

Mr. G. C. Bompas’s valuable generalizations on this fact of the number 
of meteors increasing regularly from 6 P.M. to 6 A.M., as that the number 
appearing in the East is double the number originating in the West, are given 
in a résumé at p. 131 of the volume of the British Association Reports for 
1857, held at Dublin. 


No. 5.—Mr. R. P. Greg gives the following results, taken from a catalogue 
he has constructed of the most remarkable meteors on record, as regards 
their general observed direction ; without reference, however, to the precise 
hours of observation, a matter probably of less consequence in very large 
meteors moving near the earth’s surface, than in the case of ordinary sporadic 
shooting-stars. 


Month. No. of observations. General direction. 
January ...eceee. Li N.W. to S.E. 
February ...... 20 ? 
March | <<... 13 §.E. tO N.W. 
PANU ssc ts deaees 21 N. tos. 
Bae Vi ieasde- 15 E. to w. 
AIRING Weck aancsec.. 18 P 
Ge Tak cencbaas « 14 S.E. to N.W. 
PLUSUSE f.5. casees 24 ? 
September...... 22 N.W. tO S.E. 
October ......... 19 w. to E. 
November ...... 39 N.E. to S.W. 
December ...... 15 N. to s. 


The number for each month here varies quite accidentally, as details con- 
cerning precise direction are frequently wanting in the various published 
accounts of these phenomena. 


REPORT—1860. 


22 


GEIL | LOST {OGL | 461] 211 | 66 |} FST] 801} cL |S6 | O01] L01]€01)O0T} ~"""* sTeor 
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“OSBIOAB i aad ts). iste ee Lie th > ) wae a “<2 §67 
Apyguopy | STW || 9a | ‘AN| 0 ‘qdeg | ‘Sny | Atnpyeune) Aeyy | -ady |-zepy | ‘qagq | wer 
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‘] 1avy, 
‘Sain -q'y Ag ,,‘sdoajayy snout] uo suonvasasqg ,, *9 


23 


A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 


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sodery ‘saneywneg pure yozajonty ‘yprumtpg Jo sonsoypRyep ‘sjoday uoreoossy YsHMG {toystdoy [eNUUY fsoylLoajop Jo onFopRyey s~upepyg {suoyoojop 
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Tel 90 OFS 109 SIL OPP ft sypeqe.ag ao ‘soprfog: 

69 Lt IST 6L1 O6T OLT |" Sdoaqjout Suyeuojop pur ‘soyT[O1ay 

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"fk +f. . . . * 

San | sou qandcuaed Pre a. peal aaonde Sanbane “wo drz98e(q 


‘mNSO[ICD §3aIH Ap. “[ aquy, Jo sisf{peuy 


CL | I8t Ze |oo i#8 (1s [or ie | eo jor 6 ter jez ie (qapojen%) OEST “a'V 07 OORT “a'v wos skepdsrp yetomne Jo coqum yy 


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TABLE II.—Days of the Month on which Bolides cr Aérolites have been observed and recorded.—R. P. Greg. 


24 REPORT—1860. 


1 


SH OOD 1D Hh 1D HOD OH 9 19 09 OD LD IDNA CD HINO NON SO OD HNN 


lO AHKHA OCHA RDA MANANAANMH OR AN HAHAHA 


HIOANIMDOOOAHARANMOWVAMM MAOH 121A HOA 
= oe | . 


July.| Aug. | Sept.| Oct. | Noy. | Dee. 


= 
= AAANAND 1NANOOCHNMAEOANHNAANHHAMAMDOUMWA 
3 : 
m 
o 
as) 3 3 . : Z 
; EB CODA AAAANTHA POONA AHMOANHOG Fs ENN fo 
ia) r | 
Bl acne IMMA aIeD fee imc 
am 
mm 2 F see ee 
a Oa st 500 A160 09 69 OD I OT 69 19 1D sets St NOD dH fie 
< 
rill 
ae tee ae ne ot 
oP HAH ANOMOANHANAT INHOHOHOHHANAN tin 
o e ims ie 
ey 
Ef OD OO NON DH HD 0D OV 109 OD HID CT OD HY HOD HOD SH CT 
3 rt ’ 
er) 

e Tid HS SHAS SHAD IS SKHDS SHAH SSK SSH™ 
a aN oe ee Oe Oe ee Sy ray ay ot oo ot OGG CY CG GU CLES oo, 
cS) 5 : * orm, ey eee a A Us 

fat a ered, SG: 5 srt ICY SCs Sire OT as Ba | rh ae ea 


by 


Noy. 


Oct. 


nq | 3 , : aa one) -, Sans 
S$ QU Hl SCO sr iCN COGN rsirt (2 CGNs corti 8 rt ee od 
s|n 
8 ep s : Pe ve ae A A ie rin 
ct} 3 Sia: Koy Whos Tear St Nac ae OL Pea Geers swe cn chee 
Fig ede 
= 
3 a: 
=I b Bs a a hrike rea. mune, ° alee im 
aS} | S SODCDMIIAA 5 § SIMICIQOOM sririrt 3 5 300 rr4 5 3 309 
o nas : 
a) ae) 
oS i) . : ae 
5 5 IHN AAAN PARA HA IAM EP INRA in Pi inn iN 
mn mI 
S ; 
aa =| Pie PINAR INA Pd Ha A PP INRs i iin 
| 4 
3S a | Hin . = 1a : . 
& | btw: ei) Bsr ee ee Ai 
</4 
ey Ha . Daichl aves . 
Sane AGA PHORM IMAGHA ? PHAN : 
| ren 
Sl tia tia tame fi io f fom is in ia i i 
Fy 
» 2 erin . 
& St SOT oe SS Re) ett 
Lan) 


A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 


Aérolitic epochs 
common to meteor 


Analysis of Taste II. 


Aérolitic epochs 
probably distinct 


Times of fewest 
aérolites. 


Times of fewest 
bolides. 


epochs ? from meteor epochs. 
6—10 February? | 8—10 January. Jan. 18—Feb. 6. February ...24—31. 
11—22 July. 1422 March. sAnaisly oo 20—25. | April ...... 19—26. 
4— 7 August. 5 April. April 29—May 7. OMG, Yecien 3— 8. 
- 1— 6 September. | 17—21 May. August ...21—31. | June 24-30. 
1— 5 October? 3—16 June. September 17—30, | July...... 1—10. 
9—13 November. | 3— 8 July. Dec. 16—Jan. 7. September 12—19, 


27—30 November. 
11—15 December. 


Observations on the preceding Tables, Se. 


1. While the number of bolides is considerably larger for December and 
January than for June and July, the number of aérolitic falls is about as 
large again for the latter as for the former period; the earth in her orbit 
in the first case being at her perihelion, in the latter at her aphelion. 

2. The distribution of the larger class of meteors is not so unequal 
throughout the year, if we make allowance for the immense number usually 
periodically observed in August and November, when meteors as large in 
apparent size as Jupiter, or even Venus, are not uncommon. March, May, 
June, and July furnish out of the total number generally observed of meteors 
of all sizes, the largest proportion of bolides, and especially of aérolites. 

3. There is a remarkable equality in the numbers of aérolitic falls for the 
first half of the year as compared with the second half, viz. 103 and 101 re- 
spectively. There does not appear to be any very remarkable preponderance 
in this class of meteoric phenomena during the periodic epochs for shooting- 
stars, 7.e. about the 9th of August and 10th of November. In the analysis of 
Table II. these epochs are more fully pointed out. There appear to be 
aérolitic epochs entirely distinct in themselves ; and it is worthy of remark 
that these epochs are apparently most distinctly marked, with regard to shoot- 
ing-stars and boiides only, during the first six months of the year; whilst all 
the epochs possibly common to both classes are seen to occur in the second 
six months of the year, with the single exception of one in February. 

4. Analyses of several catalogues are concisely given in Table I. for the 
purpose of convenient comparison. They vary more or less from each other, 
though not very materially; necessarily in constructing such catalogues, 
some latitude and difference of opinion may exist respecting what constitutes 
a proper bolide; and recorded observations may not always be very definite. 
If meteors of the size of Venus or Jupiter were included without discrimina- 
tion, the list of fireballs for August and November might be swelled out in- 
definitely ; e. g. hundreds of meteors of that size were seen on one night 
alone, November 13, 1833, in America. The practice of late years of look- 
ing out more particularly for shooting-stars at the usual August and Novem- 
ber periods, probably tends to increase disproportionately in all catalogues 
of bolides, the number of observations for those two months, though the 
November period appears for the present to have become very much less 
remarkable for meteoric displays than formerly. 

In constructing his own catalogue, Mr. Greg has endeavoured merely to 
insert such observations as might with most certainty be assumed to be 
remarkable for size and brilliancy. 


26 REPORT—1860. 


The catalogue itself may possibly appear in a future volume of the Reports 
of the British Association. 

An attempt has been made to separate (as aérolitic) the class of detonating 
meteors, of which more than 100 are separately given; great care having 
been taken to obtain the fullest and most accurate list of that class of me- 
teoric phenomena, as being most interesting and most important, but which 
has hitherto either been statistically too much neglected, or not sufficiently 
separated and distinguished from the class of fireballs without detonation ; 
large fireballs being frequently said to explode or burst, though when so ex- 
pressed only, it must be construed as without noise. It has likewise been 
the custom with some writers and observers to rank as aé€rolitic, all the larger 
class of fireballs, whether observed to burst with or without detunation. 
Probably one-third of the larger fireballs, 2. e. having an apparent diameter of 
15’ and upwards, burst with an audible explosion, this for those observed at 
night; of those similarly observed during daytime the proportion (according 
to Mr. Greg’s calculations) is greater, probably about one-half. It is a sin- 
gular fact, that out of 72 stonefalls, whose precise hour of fall has been 
recorded, only 13 occurred before noon, and no less than 58 fell between 
fioon and 9 p.m. Why so few should have fallen at night and before noon, in 
the morning, it is not easy to say, supposing it not to be the result of chance. 
If true that more aérolitic falls occur during daytime than during the night, 
it would seem that there is a greater tendency to encounter those bodies in 
their orbits, as they recede from the sun; that side of the earth most directly 
opposite to the sun being naturally most likely to come into actual contact 
with them. The above observations are taken for average of latitude, say 
48° north, and 10° west longitude. 

Dr. D. P. Thomson, in his ‘ Introduction to Meteorology,’ p. 302, states 
that meteors are of comparative rare occurrence in the Arctic Regions: this, 
if true, is curious and important, and deserves corroboration from some of 
the great arctic navigators now living in this country, and to whom applica- 
tion for any additional information might readily be made; the long winter 
nights in those parts being admirably adapted for observations (especially 
horary) of shooting-stars. 

The time of maximum meteor visibility being stated by M. Coulvier- 
Gravier and M. Bompas to be about 6 A.., it is rather singular that the 
times of maximum occurrence for aérolites and detonating meteors should 
be about the same hour p.m. 

5. Of the Chinese observations given by Biot, 900 were made in a period 
of only 79 years, viz. from A.p. 1023—1102; they include meteors of every 
apparent size from Jupiter to the Moon; likewise a certain number of aéro- 
lites, detonating meteors, meteoric showers, and doubtless some few auroral 
displays. The larger propurticn were observed in that portion of the sky 
included between the S.W. and S.E. 

M. Abel Rémusat, in 1819, has published other particulars, viz. of 100 
falls of stones and detonating meteors, which have been recorded likewise in 
Chinese annals, between the sixth century B.c. to 1223 a.p. In Biot’s list 
the 23rd of October presented the maximum number of observations. 

6. Further observations are to be desired respecting the zodiacal light, and 
every possible connexion between that phenomenon and that of shooting-stars 
cr meteors. Likewise further information concerning the heights at which 
meteors begin to be visible, and cease being visible. The question concern- 
ing the cause of luminosity in meteors is a highly interesting one, and still 
an open one. The phenomena displayed by the luminous trains or tails of 
shooting-stars and meteors is also a subject requiring much attention. ‘The 


DUBLIN BAY DREDGING COMMITTEE. 27 


theory that they shine by reflected solar light, has been refuted by Mr. R. P. 
Greg inthe April Number of the Philosophical Magazine. 

7. It is desirable to distinguish, if possible, between ordinary shooting- 
stars and aérolites ; Olmsted, Dr. Lawrence Smith, and Mr. Greg are strongly 
of opinion that a distinction may frequently exist, both orbital and physical. 

8. In a paper by Prof. W. Thomson in the ‘ Philosophical Magazine’ for 
December 1854, “* On the Mechanical Energies of the Solar System,” is deve- 
loped more fully the idea of Mr. Waterston, that the solar heat can only be 
maintained, on any known principle, by immense numbers of meteorites 
constantly striking the surface or atmosphere of the sun, and thus producing 
by their enormous velocity and friction a never-failing source of heat. The 
chief objection to this theory arises from the fact that, as far as we prac- 
tically know anything of meteors, so far from the probability of their being 
swallowed up in the sun goes, we see the majority of them apparently re- 
curring without waste at periodical times, and that for a long term of years: 
this simple circumstance goes much against the probability of Mr. Waterston’s 
and Prof Thomson’s theory. 

Considering that the sun’s heat, as an effect of its light, must have been 
maintained for millions of years (as proved geologically) pretty much at its 
present value, it is not improbable that future calculations, and a more accu- 
rate knowledge of the phenomena exhibited by solar light, may enable us to 
reduce considerably the supposed absolute heat of the sun, as now measured 
by ah imaginary thermometer, and thus spare us the necessity of supposing 
that its heat is so great as to require myriads of meteors to be always rush- 
ing itito it to create a fresh supply of it. If the majority of meteors should 
be, as they probably are, merely minute and gaseous comets, not possessing 
a solid or stony nature, it would still more increase the chances against 
Mr. Waterston’s theory. 

9. M. Haidinger has recently published at Vienna some valuable 
papers on the crust and external forms of meteoric stones, in relation to the 
circumstances accompanying their fall and probable condition prior to, or at 
the moment of, entering the earth’s atmosphere. 


Report of the Committee appointed to dredge Dublin Bay. By J.R. 
Krinanan, M.D., F.L.S., Professor of Zoology, Government School 
of Science applied to Mining and the Arts. 


Durine the autumn and winter months (1859) the author made several ex- 
ceursions to the bays fo the north of Dublin, the results of which will be em- 
bodied in the final Report. In the spring of 1860, finding that, owing to 
circumstances beyond their control, there was no prospect of systematic 
assistance from the other members of the Committee, the author determined 
to fix on a district to be worked systematically, and selected the series 
of bays between the Poolbeg Lighthouse and Bray as being the most Jikely 
to yield a good return as regards numberof species and variety of grounds. 
Accordingly, since the beginning of March, a series of systematic dredgings 
have been carried out in this district, the results of which are now communi- 
cated. The district may be conveniently divided into three sub-districts :— 
Ist. That between the Lighthouse wall and Kingstown east pier, including 
Kingstown Harbour. 2nd. The district between Kingstown east pier and 
the south end of Dalkey Sound, including the whole sound. 3rd. The bay 


28 REPORT—1860. 


between the latter point and Bray Head, in each case including the banks for 
seven miles off shore. 

Of these the following call for notice :— 

Bank 1.—The North Scallop bed lying about three miles off in district I. 
It consists of pure sand. Ophiurid@ are very common; Ophioconide not 
uncommon; Comatulide scarce; Asteriade not uncommon: one specimen 
of Asterias rosea, Miller (Cribella rosea, Forbes), occurred here. Other 
Echinoderms rare; Molluses are rare; Polyzoa and Tunicata are very com- 
mon; Crustacea, Decapoda, not uncommon, species few ; Amphipoda rare ; 
Cirrhipeda common; Annelida are scarce; and Polypifera very common. 
It may be generally noted, however, as unprofitable ground. 

2. Within this a bank of Pleistocene fine sand of considerable extent, but 
generally narrow in width: this contains very few living shells, but myriads 
of dead shells, from which all their organic constituents have been absorbed, 
and which are easily distinguished from the shells found in the next. 

3. The Shell Bank.—This, which I have only partially succeeded in tracing 
out, isa curious belt of broken and living shells, the dead shells being easily 
distinguished from those of the Pleistocene (Teleocene) beds. Many spe- 
cies of Crustacea are here found; Zoophytes are abundant in certain parts 
of it; Echinodermata are also common, chiefly Ophiocomide. Echinide, 
Sipunculide, and Holothuriade occur more rarely, at least to the dredge, as 
the oval tentacles of the latter are frequently brought up. This bank is 
most interesting, as it bears a close resemblance to the Turbot Bank of the 
Belfast Dredging Committee, many of the shells being identical; and one 
remarkable coral, as yet only found in the north seas of Ireland, has been 
detected in it by Mr. E. Waller (Sphenotrochus Wrightii). I have traced it 
nearly the whole way across districts 2 and 3, though in some parts its 
breadth is narrowed to a few yards; and it bears a constant relation to 
Bank 2, which in district 3 is called the “ Back.” 

4, Shanganagh Bank, a shingly, muddy, sand oyster-bed, formed from the 
influx of the river of the same name lying inside the Back in Killiney Bay.— 
Here Lupagurus levis first occurred to me; Asterias rosea, two specimens : 
Holothuriade are not uncommon ; Zoophytes and Polyzoa not uncommon. 
Of Mollusca some rare species occur here. 

5. Sorrento Bay.—This consists of dense gravelly sand. Here living 
Molluses are rare ; Nucula radiata occurs in some number, and very fine ; 
and Annelids are not uncommon ; Crustacea, except Hyade, are rare. 

6. Dalkey Sound.—This district requires almost a special description 
for itself, though not half a mile long, and barely a quarter of a mile broad, 
and the depth of water in no place, according to the Chart, exceeding at 
lowest spring tides 12 fathoms; yet species of every group are met with in 
it, which are ordinarily reputed to be deep-sea species. I have taken in it, 
and in it only, Ophidion imberbe, Pirimela denticulata, Hyas coarctatus, 
Inachus dorynchus, Ebalia Pennantii, and ynany other species which else- 
where have only occurred to me in 20-fathom water. In fact, the only spe- 
cies wanting here are those for which I would propose the name of broad 
sea species, such as Spatangus purpureus, Lupagurus levis, Inachus Dor- 
settensis, and Crangon Alimanni, none of which have ever occurred plenti- 
fully except outside the “ Back.” I defer a full description of this district 
until my final report, which I hope to present to the Association at their 
next meeting. 

7, The Cnook, a bank about seven miles from land in an easterly 
direction.—This consists of fine sand and large shells: Zoophytes are very 
common ; Oysters and Scollops also abound. Here I met several species of 


mo 


= 


DUBLIN BAY DREDGING COMMITTEE. 29 


Crustacea, which are rare elsewhere,—Lupagurus levis, Inachus Dorsettensis, 
Pinnotheres pisum, Tetromatus Bellianus, &c. The bank is not easy of 
attainment, as it requires smooth water for its proper working, and the past 
season in Dublin has been a succession of easterly and westerly gales. 

From all these grounds a number of species have been obtained ; of these, 
the Annelida and Zoophytes are yet undetermined, but the author hopes to 
put in a list of them at the next meeting of the Association. Of other 
groups, the following number of species have been determined :—Fishes, 10, 
one, Ophidion imberbe, new to Ireland: Mollusca, 188, exclusive of Polyzoa ; 
of these none are new to Ireland: Crustacea, 7); of these 5 are hitherto un- 
recorded in Ireland, 8 new to the east coast: Arachnida, 2: Echinodermata, 
$0, one, Asterias rosea, new to Dublin, &c. Spouges are omitted for the 
present. In the present immature condition of these researches, it were pre- 
mature to attempt any general conclusions; but the results as yet obtained 
go strongly to confirm an opinion advanced by the author some years since, 
regarding the absence of southern types on the Dublin coast, which occur 
further north, and which led him to the adoption of an eastern Irish or 
Dublin district, extending from Dundrum Bay to Carnsole Point. For the 
identification of most of the species the writer is responsible, with the ex- 
ception of the minute Molluscs; these Edward Waller, Esq., kindly took in 
hand—frequent recurrence of his initials in the accompanying list will show 
with what success. Great quantities of the fine sand obtained in these 
researches is yet unworked, so that it is probable that ere our next report 
other species may be added to those here given. 

To complete the work, the Committee would ask that the Committee may 
be appointed, with the addition of Edward Waller, Esq., as follows :—Pro- 
fessor J. R. Kinahan, Dublin; Dr. W. Carte; Professor J. Reay Greene; Dr. 
E. P. Wright, and Edward Waller, Esq.; and that a further sum, not exceed- 
ing £15, be placed at their disposal for this purpose, to enable them to 
COMPLETE this investigation. 


List of Species obtained in Kingstown and Killiney Bays, and a few from 
Baldoyle. 


Saxicava rugosa, living, very common. 


Psammobia Ferroensis, single valves, not 
arctica, living, not uncommon. 


common. 


Spheenia Binghami, living, one specimen : 
Dalkey Sound. 

Mya truncata, dead, not uncommon. 

arenaria, living, young specimens. 

Corbula nucleus, living, not common ; dead 
yalyes, very common. 

Lyonsia Norvegica, living, rare. 

Thracia phaseolina, living, rare, double 
valves. 

— villosiuscula, not rare. 

—— distorta, living, rare. 

on pretenue, dead, single valves 
only. ; 

Solen marginatus, dead, single valves only, 

—— siliqua, living, in Killiney Bay. 

— ensis, living, in IGlliney Bay. 

pellucidus, living, in some numbers, in 
Killiney Bay. 

Solecurtus candidus, single valves without 
epidermis: Shell Bank. 

——— coarctatus, a pair of valves: Dalkey 
Sound, 


tellinella, very common. 

Tellina crassa, very common. 

— incarnata, dead, single valves only. 

—— tenuis, living, rare. 

—— fabula, dead, single valves. 

solidula, rare, living. 

—— donacina. 

pygmeza, very rare, living. 

Syndosmya alba, common. 

Serobicularia piperata, one dead specimen, 
on Shell Bank. 

Mactra solida, rare, living here. 

—— subtruncata, one single valve. 

—— elliptica, very common. 

—— stultorum, rare here. 

Lutraria elliptica, dead, shells only. 

Tapes decussata, uncommon. 

pullastra, not uncommon. 

virginea, very common. 

Venus casina, uncommon. 

striatula, rare here. 

——- fasciata, common. 


30 REPORT—1860. 


Venus ovata, common. 

Artemis exoleta, common. 

lincta, not uncommon. 

Lucinopsis undata, rare. 

Cyprina Islandica, common, dead; not 
common, living here. 

Circe minima, E. W., very rare. 

Astarte sulcata, uncommon. 

triangularis, EH. W., not uncommon. 

Cardium echinatum, not uncommon, dead ; 
living small, rare. 

edule, rare here. 

— pygmzum, uncommon. 

—— Norvegicum, not uncommon. 

—— nodosum, very common. 

—— fasciatum, common. 

Lucina borealis, common. 

flexuosa, Killiney Bay, rare. 

spinifera, one single valve. 

Montacuta bidentata, H.W. 

substriata, on Spat. purpureus, 

Kellia suborbicularis, rare. 

rubra, E. W. 

Lepton nitidum, BH. W. 

squamosum, single valves, rare. 

Mytilus edulis, common. 

Modiola Modiolus, common. 

Crenella discors, common. 

marmorata, uncommon. 

Nucula nucleus, very common. 

— nitida, common. 

radiata, not uncommon, but local. 

Leda caudata, rare, living. 

Pectunculus glycimeris, living, rare and 
small; dead, large and uncommon. 

Lima Loscombii, rare. 

Pecten varius, rare. 

pusio, rare. 

—— tigrinus, not rare. 

maximus, not rare. 

opercularis, very common. 

Ostrea edulis, very common. 

Anomia ephippium. 

patelliformis. 

— striata. 

Chiton fascicularis, rare. 

—— marmoreus, rare. 

asellus, very common; other species 

et undetermined, 

Patella vulgata. 

—— pellucida. 

athletica, 

Acmza virginea, common; Dalkey Sound. 

testudinalis, 

Dentalium entalis, uncommon. 

tarentinum, dead, only fragments, rare, 

Pileopsis Hungaricus, rare here. 

Fissurella reticulata, uncommon. 

Emarginula reticulata, uncommon, 

Trochus zizyphinus. 

granulatus. 

Montagui, 

—— tumidus. 

— umnbilicatus. 

cinerarius. 

—— millegranus. 


Trochus magus, broken. 
helicinus. 

—— pusillus, H.W, 
Phasianella pullus. 
Adeorbis subcarinata. 
Littorina littorea. 

rudis. 

littoralis. 

Lacuna vincta. 

crassior, Shanganagh. 
Rissoa Beanii, H.W., one fragment. 
uly. 

— costata. 

parva. 

labiosa. 

—— punctura, E. W. 
inconspicua, E. W. 
semistriata, HE. W. 
soluta, one specimen, 
vitrea. 

striata. 

striatula, E. W. 
Skenea divisa, E. W. 
planorbis. 
Turritella communis. 
Cecum glabrum, EH. W.. 
Aporrhais pes-pelecani, 
Cerithium. 

adyersum, E. W. 
Scalaria Turtonis, broken. 
communis. 

Eulima polita, B. W. 
distorta, EH. W. 
bilineata, E. W. 


Chemnitzia fulyocincta: Shell Bank. 


elegantissima, E. W. 
indistincta, H. W. 
Odostomia eulimoides. 
insculpta, E. W. 
—— interstincta, E. W. 
spiralis, E. W. 
decussata. 

Natica monilifera. 
nitida. 

sordida. 
Velutina levigata. 
Murex erinaceus. 
Purpura lapillus. 
Nassa reticulata. 
incrassata, rare. 
—— pygmea. 
Buccinum undatum. 
Fusus antiquus, 
Islandicus. 
propinquus. 
Trophon Barvicensis, 
—— muricatus, 
clathratus, 
Mangelia turricula, 
—— rufa, 
septangularis. 
— linearis. 

—— nebula. 

—— costata. 

Cyprza Europa. 
Cylichna cylindracea. 


A 


DUBLIN BAY DREDGING COMMITTEE. 


Cylichna truncata, E. W. 


Amphisphyra Hyalina. 
Tornatella fasciata. 
Akera bullata. 
Scaphander lignarius. 
Philine aperta. 
Aplysia hybrida. 


Pleurobranchus membranaceus. 


-—— plunula. 

Eolis papillosa. 
Tritonia Hombergii. 
Doto coronata. 
Pholas dactylus. 
crispata. 
Aplidium fallax. 
Botryllus polycyclus. 
Ascidia mentula. 
— virginea. 
Molgula tubulosa. 
Cynthia aggregata. 
Hledone cirrhosus. 
Rossia macrosoma. 


Stenorhynchus phalangium. 


Inachus Dorsettensis. 
dorynchus. 
Hyas araneus. 

= coarctatus. 
Eurynome aspera. 
Cancer pagurus, 
Pilumnus hirtellus, 
Pirimela denticulata. 
Carcinus mzenas. 
Portunus puber. 
arcuatus. 

—— depurator. 
— holsatus. 

—— pusillus. 
Pinnotheres pisum. 
PEbalia Pennantii. 
Atelecyclus heterodon. 


Corystes Cassivelaunus. 


Pinnotheres pisum. 
Eupagurus Streblonyx. 
—— Prideauxii, 

— Cuanensis. 

— Ulidianus. 

—— Thompsonii. 
Porcellana longicornis. 
platycheles. 
Galathea squamifera. 
— strigosa. 

—— Andrewsii. 

—— nexa. 

— dispersa. 
Palinurus vulgaris. 
Homarus vulgaris. 
Crangon vulgaris. 
— fasciatus. 

— sculptus. 

— Allmanni. 

— bispinosus. 


Nika edulis, 


Detailed notes on the species will accompany the final Report. 


Hippolyte yarians. 
—— Cranchii. 

—— Thompsonii. 
—— pusiola. 
Yarrellii. 
Pandalus annulicornis. 
leptorhynchus. 
Palzemon serratus. 
— squilla. 
varians. 
Athanas nitescens. 
Lysianassa longicornis. 
Anonyx denticulatus. 
Ampelisca typicus. 
Urothoe marinus. 
elegans. 
Iphimedia obesa. 
Eblane. 
Acanthonotus testudo. 
Dexamine spinosa, 
Gammarus locusta. 
— fluviatilis. 
palmatus. 

—— Othonis. 
longimanus. 
Amphithoe rubricata, 
—— littorina. 
Podocerus falcatus. 
variegatus. 
Corophium longicorne. 
Chelura terebrans. 
Hyperia Galba. 
Caprella tuberculata. 
Comatula rosacea. 
Ophiura texturata. 
—— albida. 
Ophiocoma neglecta. 
Ballii. 

bellis. 

rosula. 

minuta. 
Uraster glacialis. 
—— rubens. 

— violacea. 
hispida. 
Cribella oculata. 
rosea. 

Solaster papposa. 
Asterias aurantiaca, 
Echinus sphera. 
— Miliaris. 


Echinocyamus pusillus, 


Spatan urpureus. 
ee hiaee cordatus. 
Cucumaria fusiformis, 
Hyndmanni. 
Thyone papillosa. 
Synapta inherens, 
Syrinx Harveii. 
granulosus. 


Sipunculus Bernhardus. 


Priapulus caudatus. 


31 


32 REPORT—1860. 


Report on the Excavations in Dura Den. 
By the Rev. Joan ANDERSON, D.D., F.G.S. 


In reporting on the operations and researches in Dura Den during the 
summer of 1860, the Committee laid open several large sections of super- 
incumbent boulder clay and of the underlying yellow sandstone, but were 
unsuccessful in obtaining any of the Pamphractean or Pterichthyan forms 
sought after. None of the workmen engaged in the excavations in 1837, 
when these organisms were found in great numbers, were living in the di- 
strict ; and the Committee, proceeding on the information of others, failed to 
detect the precise fossiliferous bed in question. Their labours brought them, 
however, to a point which cannot be far distant from these crustacean trea- 
sures, and they are hopeful that, on resuming their researches, they shall 
meet with the desired success. They proceeded to other sections of the rock, 
in the bottom of the ravine, and there they were richly rewarded with an 
abundance of the fossil remains of fishes, chiefly of the genus Holoptychius 
and other Celacanths. 

The yellow sandstone deposit, as described in the ‘Course of Creation’ 
in former papers of Dr. Anderson, consists of an alternating series of grits, 
shales, marls, and fine-grained sandstone, of various shades of colour. The 
fossil fishes are confined to one particular bed, which, when laid open, easily 
splits up, the organic materials determining the point of separation, and 
exhibiting often on a single flag from fifty to a hundred closely-packed and 
well-defined figures with scales, fins, and cranial plates quite entire. On the 
present occasion your Committee were surrounded by an intelligent group of 
lovers of the science, male and female, from Edinburgh, St. Andrews, Forfar, 
Dundee, and Cupar, and succeeded, after a few hours’ labour, in displaying to 
their eager gaze some of the largest and most beautiful specimens of these 
older denizens of our seas. 

It will not be necessary to describe in detail any of the well-known forms 
and characteristics of Holoptychius, the most abundant of the genera found in 
this deposit. But having submitted some of the most perfect of the spe- 
cimens to Professor Huxley, and as he thereby was enabled to detect some 
new particulars connected with the structure and figure of the genus, it will 
not be deemed out of place to give an abstract of his interesting descrip- 
tion, contained at length in Dr. Anderson’s ‘ Monograph of Dura Den*.’ 

“Tn studying,” says Professor Huxley, “ the new forms of Devonian fish 
which have been described, I found it desirable to obtain a more definite 
conception than was deducible from extant materials, of the characters of 
Holoptychius. To this end I examined a considerable number of specimens 
of Holoptychius Andersoni, contained partly in the collection of the British 
Museum, partly in that of the Museum of Practical Geology, and I have 
arrived at the following conclusions. Holoptychius Andersoni has very nearly 
the proportions of a carp, but its body is thicker and its snout is more rounded 
from side to side. ‘The greatest depth of the body is in front of its middle ; 
the length of the whole body is to that of the head nearly as five to one. 
The orbit is nearly circular, about one-fourth the length of the head. The 
cranial bones all exhibit a peculiar granular structure. The two parietals 
occupy a large extent of the upper wall of the cranium, and have the form 
of pentagons with their elongated bases turned inwards and applied to one 
another. The occipital region is covered by three bones, one median, and 
two lateral; the lateral bones having radiating striz on the posterior halves 


* Dura Den; A Monograph of the Yellow Sandstone and its remarkable Fossil Remains. 
By the Rey. J. Anderson, D.D., F.G.S, Edinburgh: Thomas Constable and Co. 


ON THE EXCAVATIONS IN DURA DEN. 33 


of their outer surfaces. The operculum is a broad bone, larger behind, 
where it is convex, than in front, where it is concave, and much longerthan 
it is deep. 

_ “The rami of the lower jaw are stout and strong, and form a very broad, 
almost semicircular arch. The characters of the scales are well known. 
The fins are lobate, and the dorsal fin is small and triangular. Sir Philip 
Egerton, in a valuable memoir recently read before the Geological Society, 
_expresses his belief that Holoptychius has two dorsal fins. I am very loath 
to controvert the opinion of so experienced and skilful an observer, the more 
particularly as specimens of Holoptychius with perfect tails are very rare, 
but one or two complete examples I have seen, leave no room in my mind 
for any other conclusion than that stated above.” 

Numerous perfect specimens of this remarkable fish have been obtained 
in our recent excavations, which show the lobate character of the fins as de- 
scribed by the learned Professor, as well as the unity of the dorsal organ. 
The entire form of the body of Holoptychius is likewise beautifully deve- 
loped in some of the specimens, where the caudal end appears gradually 
tapering toa point, and not at all dent up as represented in all former de- 
scriptions ; while the ventral lobe of the caudal fin, though rather shorter than 
the dorsal lobe, has nearly the same depth, and not in the ordinary sense 
of the heterocercal structure. 

In the course of our explorations we also succeeded in obtaining several 
perfect specimens of two new and hitherto undescribed genera of Ceelacanths, 
namely, Glyptolemus Kinnairdii and Phaneropleuron Andersont. 

The specific distinction of Glyptolemus Kinnairdit was proposed and 
adopted at the Meeting of the London Geological Society in honour of 
Lord Kinnaird, whose zeal in promoting the interests of geology is only 
equalled by his enlightened endeavours to advance the interests of anything 
connected with our social and industrial well-being as a statesman. The 
generic term of Glyptolemus was suggested on account of the marked 
sculpture of the jugular plates in one of the specimens. As described in the 
“Monograph” of Dura Den, the scales and fins likewise form strongly 
marked characteristics of this new genus. 

The scales are rhomboidal, and have an average short diameter of one- 
sixth of an inch. Twenty-four series are visible, and diverge from the me- 
dian line in the ordinary way ; they are larger on the anterior part of the 
ventral surface than on the posterior part, and at the side of the body than 
on the belly. They are pitted and ridged almost as in Glyptopomus, although 
somewhat thinner and less bony than in that fish. There are two dorsal fins 
which are situated very far back, the anterior edge of the root of the first 
being nine inches distant from the end of the snout in one of the specimens : it 
is remarkably slender, and of a semi-oval outline. The second dorsal fin is 
considerably larger than the first, being two inches on its longest axis, and 
its breadth about an inch in depth. The entire length of the body, in several 
of the specimens, varies from a foot and a half to nearly two feet. 

The other new genus discovered in the course of our explorations is the 
Phaneropleuron Andersoni, and from some very imperfect fragments named 
by Professor Agassiz as a Glypticus, but without describing or defining the 
genus. The generic appellation, now bestowed by Professor Huxley, ex- 
presses the most striking character of the fish—the curious development and 
obtrusiveness of its ribs, arising from their complete ossification as well as 
_ the thinness of the scales. The affinity of Phaneropleuron with the typical 
ceelacanths is indicated not only by its singular tail, but by its persistent 
ohh by its lobate pectoral and ventral fins, and by its well-ossified 
0. D 


34 REPORT—1860. 


superior and inferior vertebral elements. The scales remind one of Holo- 
ptychius, but are much thinner and differently sculptured. ‘The fins are more 
nearly of the structure of this genus in theirgeneral facies, though they differ in 
details. They are lobate in the lateral pairs, a character now regarded by one 
of our most eminent ichthyologic authorities, Sir Philip Egerton, as belonging 
to the entire family of Ccelacanths, and which Agassiz has also described 
in his elaborate account of the Glyptolepis of Clashbennie in the ‘ Poissons 
Fossiles.’ 

This locality, so richly stored with these and other forms of fossil remains, 
has now contributed largely to our stock of paleontological knowledge. 
Should the researches be continued, your Committee are sanguine, not only 
in the recovery of the long-lost bed of the disputed Pamphractus, but like- 
wise of new genera and new species still sealed up in the yellow sandstone 
museum of Dura Den*. Trilobites of a small type, Productz and Spirifers, 
are very numerous in the carboniferous shales of Ladeddie, which are in 
immediate superposition and stretch along the southern opening of the Den. 
About three miles to the eastward, in the irenstone deposits of Denbre 
and Mount Melville, large jaws, teeth, bones, and scales of the genus 
Rhizodus are in the greatest abundance and the most beautiful preservation. 
Thus the geologist may here study successively the upper beds of the Old 
Red Sandstone, the Mountain Limestone, Ironstone shales, and the Coal-mea- 
sures on the most northern limits of the Carboniferous system. Trap-rocks 
everywhere penetrate the series of sedimentary deposits, indurating the sand- 
stone, fusing the limestone, roasting the coal, and exhibiting proofs of those 
destructive agencies and deleterious impregnations by which the fishes of 
Dura Den were suddenly overtaken, silted up, and preserved in such num- 
bers and perfect forms in their stony matrix. 


Report on the Experimental Plots in the Botanical Garden of the 
Royal Agricultural College, Cirencester. By James BuckMAN, 
F.L.S., F.S.A., F.G.S. &c., Professor of Botany and Geology, Royal 
Agricultural College. 


In presenting our Report for 1860, it will be necessary to remark, that on 
account of the peculiarities of the season, particularly its latetiess, and the 
fact of the unusual period of the Oxford Meeting, the Report before the 
Section at Oxford was made verbally, permission having been obtained to 
make a more full and written report when the experiments had attained to 
something like completion. It was reported before the Section that 200 
plots were in operation, which were classified as follows :— 


Plots 

Agricultural Plants........ Ss ortsticnt one OO 

Medical PiiGs. ieee as sre te weet es Se 
Psculent Vepetaples 2s"... c.p2c05 00 os 20 

Grasses, old and new plots............ -- 60 

Miscellaneous Plants <2 2.2... 20s>.: 22. 40 

Total 200 


Of these, at the Oxford Meeting it was reported that more than half were 
either new seeds only just germinated, while for the others they had made 


* See Reports of the British Association for 1858 and 1859. 


ON THE GROWTH OF PLANTS. 35 


so little progress, that we almost despaired of any substantial results under 
such untoward circumstances. Still, however, we now offer remarks upon 
some of the more striking experiments, which it may be said are so far com- 
plete up to November. 


GRASSES. 


Sorghum saccharatum (Holcus saccharatus), Chinese Sugar-cane-—The 
fine summer of 1859 enabled us to grow this plant to a height of as much 
as 7 feet, as also to perfect its saccharine matter, at least in a very high 
degree. This success, which was pretty general all over England, had caused 
very flattering encomiums to be passed on the merits of this plant for agricul- 
tural purposes, especially as a green soiling food. The total failure, however, 
of our experiments for this season is not only instructive as to the great 
diversity of seasons, but should also teach us caution in recommending the 
extensive adoption of any new plant in our uncertain climate from only a 
single year’s growth. Our best plants did not attain 6 inches, and indeed our 
failure this year was more signal than our success the previous one. 

fgilops ovata.— Although our specimens are far later in coming to matu- 
rily than in any former season, yet the results are more striking than we have 
before observed. Even at the time of our writing (November), little of our 
crop for 1860 has ripened; but the spikes are longer than usual, whilst the 
stalks (culms) are taller; and added to this is the important result of a show 
of more and larger grain, of the shape of the wheat grain, so that we have 
searcely a doubt left as to this being the parent of the cereal or corn wheat. 
Again, as another evidence of the results and effects of cultivation, we have 
the crop of this year affected with all the epiphytical fungi to which wheat 
is liable, and the more so the more it is manured. 

Gyneria argentea, Pampas Grass.—-Our specimens, one of which flowered 
most beautifully last year, are all dead, so that however highly this plant 
may be recommended for naturalization in other parts of England, where the 
climate is milder, we cannot think it will ever be safe to trust to it on the 
“Stony Cotteswolds.” 

Of British Grasses, we have to report that we have had in operation during 
the present season as many as sixty plots; several of these are only our usual 
common English species, many of which are condemned to be resown on 
account of their inevitable admixture. Among the experiments of interest, 
we have to report the complete production of Festuca elatior from a plot of 
F, loliacea, in which the changes were as follows :— 

2nd year.— Festuca loliacea the rule, with exceptional cases of F’. pratensis. 

3rd year.—Festuca pratensis the rule, with exceptional cases of £’. elatior. 

4th year.—F. elatior increased. 

5th year, 1860.—Festuca elatior has complete possession. 

In reference to this, it will be remembered that we noted in a former 
Report the occurrence of F. elatior in Earl Bathurst's Park, which we then 
conjectured had been derived from the sowing of the seed of FP. pratensis. 
This year we have further to remark that here the e/atior form is the rule, 
and scarcely a vestige of the F. pratensis remains ; and very coarse and un- 
sightly it is as a glade in a park. 

We have now performed this experiment twice with the same result, and 
our views seem confirmed by the accidental case just referred to; we have 
then no doubt that the three forms just adverted to are but varieties of a 
single species ; and we have much pleasure in observing that our views in 
this and other cases of alike kind, derived from actual experiment, and 
reported upon to the Association in 1847, should be confirmed by the 

D2 


36 REPORT—1860. 


Specific Botanist as thus: under the head of ‘Meadow Fescue, Festuca 
elatior,’ see Bentham’s ‘ Handbook of the British Flora,’ p.602, we have the 
following :— 

“a. Spiked Meadow Fescue (fF. loliacea, Eng. Bot. t. 1821). Spikelets 
almost sessile, in a simple spike. Grows with the common form, always 
passing gradually into it. 

“b. Common Meadow Fescue (F. pratensis, Eng. Bot. t. 1592). Panicle 
slightly branched but close. In meadows and pastures. 

“ce. Tall Meadow Fescue (F.elutior, Eng. Bot. t. 1593 ; & arundinacea, 
Bab. Man.). A taller, often reed-like plant, with broader leaves, the panicle 
more branched and spreading. On banks of rivers, and in wet places, espe- 
cially near the sea.” 

Now, though well aware that these views are not generally shared by col- 
lecting botanists, we are yearly more and more persuaded that even greater 
innovations than now contended for y.ill be admitted; and we cannot help 
expressing pride and pleasure that we should for the last fourteen years 
have been conducting a series of experiments, many of which practically 
prove the truth of several of the theoretical views, with regard to what has 
been termed the “lumping” of species, of the author of the Handbook ; 
and we cannot here omit expressing our best thanks to the British Association 
for their assistance in prosecuting these interesting inquiries. 

Poa ( Glyceria) aquatica.—Our plot with this experiment still continues 
to exhibit 27 its entire space, without the slightest intermiaxture, the induced 
form we have before reported upon, which indeed is so different from the 
original grass, that at a first glance most observers would pronounce it to be 
large examples of Poa trivialis ; the differences, however, in all parts are as 
great between our induced form and that grass, as exists on comparing the 
induced form with the Poa aquatica. There can be no doubt that in 
this case the cultivation of the seed of a water grass in an upland situation 
has led to great changes, not, as has been supposed, brought about by cross- 
breeding or hybridizing, but the seed of the P. aquatica has at once been 
changed in the growth of the plants that came up from it ; and it now remains 
to see if the change be a permanent one, to which end we hope to be able 
to sow a plot of the seed of the induced grass next spring; but in the mean- 
time it may be well to remark, that although it has frequently seeded, yet 
that the bed is still free both from innovations from seedlings of its own kind, 
as also from those of other species. 

Poa (Glyceria) fluitans.—At the same time that the plot was sown with 
the seed of P. aquatica, another plot was occupied with seeds of the Poa 
Jluitans ; and we should remark that in both cases the seeds were drilled, and 
the drills remain intact to the present hour. Now the result is, that both 
plots were indistinguishable at the first time of flowering, and have so re- 
mained to the present hour; and with reference to the last form, it may be 
well to point out that, having been favoured by Messrs. Sutton of Reading 
with specimens of the collection of grasses which they keep in cultivation, a 
bundle marked ‘‘ Glyceria fluitans” is identical with our induced forms from 
both P. aquatica and P. fluitans. 

Poa aquatica and P. fluitans.—We offer no explanation of these; being 
wellacquaiuted with these two species, we can truly say that our induced form 
is widely different ; nor is it at all identical with any other British species. It 
is, however, still a matter of regret that we have not been able to procure 
ripe seed of these species from the district, as, so far as we can discover, none 
of the P. aquatica at least has ripened in the district. It may be well to 
mention, that even this shyness in the ripening of the seed of this now so 


i 


ON THE GROWTH OF PLANTS. 37 


emphatically a water grass, is not without value as affording something like 
evidence that this species is perhaps after all out of place, and this may 
point to the fact that our induced form is the right one; at all events, it quite 
determines the fact that the name Glyceria is inapplicable, as it is a decided 
Poa in cultivation. 


Crop PLANTs. 


Pastinaca sativa, Parsnip.—Our ennobled examples of these were con- 
sidered so perfect, that it was thought advisable to consign the whole of the 
seed of 1859 to the Messrs. Sutton of Reading, as new varieties of any cul- 
tivated crop plant is always desirable, and more especially when, as in the 
present case, the new form has been directly derived, not from a variety, but 
from the original wild stock. In reference to the continued success of this 
experiment, Mr. Sutton reports in a letter of October 17th of this year as 
follows :— 

“ The Student Parsnip in our trial ground is the nicest shape of any, more 
free from fibres, and as large as the ‘ hollow crown,’ which is a good medium 
size. The flavour seems to be very nice.” 

This is the more important, as of late this useful garden esculent has much 
fallen into disuse, its want of flavour being the assigned cause. 

We must not omit to remark, that one of the most malformed specimens 
of parsnip, and also a highly digitated Swedish Turnip, were set aside for 
seeding, with a view to sowing next spring in the same kind of plots, as there 
seems reason to expect that such degenerate forms could only beget a 
degenerate progeny : with a view then to ascertain how far this degeneracy, 
or otherwise, may proceed, we first took careful portraits of the seeded roots, 
the seed of which is now put by for experiment. : 

Brassica oleracea—Having gathered some seeds of this wild cabbage 
from Llandudno, N. Wales, in August 1859, we sowed it in the summer of 
the present year in our private garden, from whence we removed some plants 
for a plot in our College garden. These, and our own examples, are already 
highly curious, as showing the tendency to run into so many of the cabbage 
varieties, e. g. long petioles ; the types known as “kale, greens,” &c., both 
with broad, more or less undivided leaves, and with a tendency to deep lobes 
and divisions. Others with short petioles, offer the true cabbage type; while 
these even now show tendencies for the production of sorts, as flat heads, 
sugar-loaf, green, red, and white varieties. These of course are what one 
would expect, but still it is curious to mark its progress. 

In speaking of the Brassica family, we cannot help expressing our conyic- 
tion of the justice of including the genus Stnapis with Brassica ; for just as 
our experiments incline us to the opinion that all our so-called species of 
this genus are after all only derivatives, so we believe that the Charlock 
Sinapis arvensis, L. is also an agrarian form of Brassica. Upon this, however, 
we want the experiments of a lifetime; still these would be replete with 
interest, and more especially as we find cabbage, rape, turnips, radishes, 
and mustard almost wholly attendant upon cultivation, and that not only 
with us, but in every variation of climate. How wild the thickets of Sinapis 
nigra, some 6 feet high, look on the banks of the Ohio! and yet we have the 
authority of Beck in favour of its introduction from Europe ; and so we have 
evidence of the crops in India being smothered with wild rapes, which our 
experiments show are principally Judbless varieties of the turnip. 

Mangel Wurzel——The inquiry connected with the growth of this crop 
is one which may be considered of interest in a physiological as well as an 
agricultural point of view, and hence we give its results in this place. 


38 REPORT—1860. 


It is tolerably well known that this valuable crop was introduced into 
cultivation with the hope that it would yield a valuable supply of food in the 
shape of leaves, whilst at the same time it was supposed to be capable of 
fully developing its growth of roots, the leaves then being employed for 
summer and autumn food, whilst the roots were to be stored for winter use; 
however, we were early struck with the fact, that using the leaves to any 
extent, would prejudice the crop of the roots, and we therefore twice before 
the last year instituted experiments upon this matter with a result that may 
be generally stated as follows. 

The Mangel Wurzel, stripped of its outer leaves from two to three times 
during their period of growth, do not produce half the weight of root of those 
left intact. 

And herein we thought that we had established the law, that as long as a 
leaf of Mangel was sufficiently sound to be useful as food for any animal, so 
long was it of use in aiding the proper development of the plant; but this 
statement has been controverted by the result of some experiments made at 
the Albert Agricultural Model Farm, Ireland, where it is stated that the 
result of taking the enormous quantity of 5 tons of leaves from the acre of a 
growing Mangel crop, was to increase the weight of roots at the rate of nearly 
54 tons. Now, under these circumstances we determined upon repeating the 
experiments upon a larger variety of Mangels this year. 

Ist. A set of experiments made with nine sorts of Mangel Wurzel planted 
with burnt ashes, duly thinned and tended as usual; the plots being 24 
yards square. 

2nd. Nine plots of the same sorts transplanted. 

The outer leaves of all these plots were taken off on the two following 
dates, September 4 and September 21. 

On the 12th of November the whole crops topped and tailed, consisting of 
twenty-four roots to each bed, half of which had been stripped of their outer 
leaves; thus twelve roots each, stripped and unstripped, gave the following 
results for both the untransplanted and the transplanted plots :— 


Untransplanted Plots. / Transplanted Plots. 

Names. Entire. |Stripped. | Entire. |Transplanted. 
lbs. oz. | Ibs. oz. lbs. oz. Ibs. 02+ 
J. Elvethan .0......cececcessccvcsessesese 8°10 at ea 14°10 5°10 
DopVellow, Globe; .c.testecsec enessvarcses peta D° 2) |: Seale ela 6:14 
Be med Glove 087. e lites eset 8 2 CAD OB Vis 3 
4. New Olive-shaped Red Globe...... 11:13 7°60) 44 12° 4 5: 6 
5. New Olive-shaped Yellow Globe 16°13 12.33 seo 11°14 7°10 
6. Sutton’s New Orange Globe ...... 9-5 312.) 6 10° 2 5: 3 
7. Improved Long Yellow .........++. 19: 0 Ol | 7.) 1910 We. 
1 8. New Long White ......ceccccecssecee es aoe 7 8 8 12°11 7 6 
Of SH VSMC ions zetcieen a deed sass cosas 16°15 So @) | 9 15°13 611 
OtB eee ppcxsostteeee meee Boner os 114°10 63° 3 121: 4 63° 6 


Here then we take these results from so many sorts as conclusive evidence 
upon this point, only remarking that, in all probability, had the season been 
one of an ordinary kind, the discrepancy would have been even greater, as 
this year the tendency of growth has been in favour of leaf development. 

The same experiments were tried with Kohl Rabbi, and withthe like results ; 
and it should be mentioned, with regard to all of them, that the seed was 
obtained from the Messrs. Sutton of Reading, and that it was true to sort. 


ON THE GROWTH OF PLANTS. 39 


It s not a little remarkable that in both the Mangel and Kohl Rabbi the 
results have been greater in the transplanted than in the untransplanted plots, 
the former yielding a larger crop; this too has probably been favoured by 
the moist season, but as it is a subject of great farming interest, we shall 
renew our experiments upon this matter. 

Dipsacus fullonum et sylvestris.—Our plot of this year fully confirmed our 
view of last year, as to the specific identity of these two forms of this plant; 
for without being able to assert that we had decided D. fullonum from the 
seeds of D. sylvestris, or the opposite, yet the specimens glided soimperceptibly 
into either form, that, distinct as are decided examples, we were much puzzled 
in deciding as to the paternity of some of our specimens. 

To quote from English Botany, 2nd edition: ‘“ Hudson mentions this plant 
as growing about hedges. Inthe clothing countries, where it is cultivated 
for use, it may escape from the fields. There is much doubt concerning the 
value of its specific difference from the D. sylvestris.” 

Bentham is of the same opinion, so that our experiments in this only lay 
claim to a simple and practical method of confirming these views. Our 
notion at the same time is that it would be exceedingly difficult to find a 
wild example of the true D. fullonum ; that is, one which from its hard re- 
flexed bracts would be worth anything for fulling purposes. We have hunted 
long in the districts where the economic form of the Teasel is grown, and we 
have always been of opinion that where its seed has been scattered and allowed 
to grow wild, it lost its stiff hooked characters ; and, to say the least, even the 
best of them merged into D. sylvestris ; the fullonum being indeed a difficult 
plant to keep perfect, unless under constant change of seed and soil. 


WEEDS, &c. 


Thistles have formed the subject of several experiments during the past 
year, which will be referred to under the following names :—Carduus 
arvensis, C. acaulis, vars., C. tuberosus. 

Carduus arvensis.—Our experiments upon the growth of this plant were 
undertaken in order to explain their method of reproduction, as it had been 
disputed by the farmer that thistles were produced from seed. 

On September 2nd, 1859, were sown ten seeds which had been collected 
a few days previously ; by the 21st of the month these had all come up, and 
some began to show the secondary leaves, as in Diagram, fig. 1. By the time 
the prickly foliage became manifest, the cold weather had set in and all the 
plants apparently died. However, in February 1860 we noticed a bud just 
emerging through the soil, which induced us to take up a couple of the speci- 
mens and make drawings of them, of which copies will be seen at 2a and 2b. 

Here then at a and 6 are buds by which the continuance of the plant is 
secured, the buds a, 6 forming whilst 5, b are sending up leaves for the second 
year, so that by June the plants had advanced to the condition of fig. 3, in 
which, while a strong shoot is progressing above ground, a most extraordinary 
rhizomation is taking place below fig. 3, fully explaining how in the next 
season we may meet with a thicket of Thistles derived from a single plant. 

Here then it is obvious that the conclusions with respect to the Thistle not 
seeding, were the result of the small and inconspicuous plant which it makes 
the first year, and this apparently «lying, confirmed this view ; however, we 
see from this experiment that thistle seed is as fecundate as that of other 
plants, and as we have counted as many as 150 seeds from a single head of 
flowers, and as we may haye an average of ten heads of flowers to a single 
flowering stem, the eight tertiary buds at fig. 3 a, a may each represent a 


40 REPORT—1860. 


flowering head in the following season, which would thus give us the following 
sum as the seeding capabilities of a single Thistle plant, namely— 
150 x 10 x 8= 12000. 

These figures then will account for the “ Plague of Thistles” which one 
sometimes hears of, and points out most forcibly the importance of not 
allowing these plants to perfect their seed, and hence waste places and 
neglected waysides should carefully be watched in this respect ; but as this 
cannot adequately be done without compulsory enactments, it is interesting 
to find that some of our colonies have already instituted state laws with 
reference to this subject, and during the last Session of Parliament an attempt 
was made to get an act applicable for this object for Ireland. The destroying 
of such thickets of Thistles as we have described has ever been an object of 
interest with the farmer; and it is not a little curious to remark that the 
operations connected therewith have so much been regulated by rhyming 
directions, as follows :— 

‘ Thistles cut in April, 
Come up in a little while; 
If in May, 

They grow the next day; 
If in June, 

They ’Il grow again soon ; 
If in July, 

They ’ll hardly die; 

If in August, 

Die they must.” 

These words, uncouth as they are, are still meant to express some important 
facts in the natural history of the plant. It may be observed that, with the 
preparation we have described of underground buds, there can be no wonder 
at the quick reappearance of the plant on early cutting ; at the same time, 
if we consider that the whole of the aboveground parts of the plants 
would naturally die at the first approach of cold, we may conclude that the 
decree of 

“Tf cut in August, 

Die they must ”’ 
is more apparent than real. For while the tertiary buds are advancing to 
flower, they are also active in providing a still newer growth of rhizomata and 
buds to perpetuate the continuance of the plant; and hence we have no hesi- 
tation in saying that never can this thistle be destroyed by late cutting off its 
aboveground stems. However, even at this time much good may be done 
in keeping down the reproduction of the plant; for by the August mowing 
seeding is prevented, though even for this object we should prefer an earlier 
cutting, as one head of flowers usually ripens at a time, and not all at once. 

Carduus acaulis—We last year reported upon our experiments with the 
true acauline form and the slightly cauline examples of this species ; we have 
now to remark that the acauline examples maintain their normal condition, 
whilst the cauline ones, from being only about 3 inches high when selected 
for the experiment, have this year advanced to a complete thicket of stems 
nearly a yard high, some of which have as many as a dozen heads of flowers, 
and is a very showy and handsome plant. 

Carduus tuberosus.—The specimens originally discovered by us at Ave- 
bury Druidical Circle have now advanced to immense masses, both as regards 
their summer development of flowers and their tuberous rootstocks; the 
flowers are above 3 feet high, much branched and very showy, very different 
from the single, or at most two-headed flower-stems of the ‘ English Flora,’ 
pl. 2562, which, however, is a faithful representation of the plant we trans« 
ported to our garden. The tubers with us are as large as those of Dahlias. 


ON THE GROWTH OF PLANTS. 41 


We should remark that this year we have a number of seedling plants which 
have come up wildly in different parts of our experimental garden, which we 
shall be curious to know if they become like their parents. With us it seeds 
so enorniously, that it can hardly fail to be a matter of interest as to how this 
plant, originally noticed as from Great Ridge between Boyton House and 
Fonthill, Wilts, should have been for so many ycars lost to our flora, whilst its 
present natural habitat on artificial earthworks, though truly ancient enough, 
would seem to point to its having been introduced to its present locality. 


Diagram showing the mode of Growth of Carduus arvensis. 


} 
f \ 77 Feb. 17, 1860. } 
mee ee 


3rd nat. size. 


Fig. 1. Seedling of the first year. 

Fig. 2. a & b. The position of the seedling plants in spring sending up secondary buds J, d. 

Fig. 3. The secondary shoot advanced to a large plant, while the rhizome extends and ter- 
tiary buds a, a are prepared for the following year. 


Bentham, in his description of the position of this plant, has the following 
remarks :— 

“Tn moist, rich meadows, and marshy, open woods, in western and south- 
central Europe, extending eastwards to Transylvania.” 

Its position at Avebury is so very different from this, that we cannot for- 
bear to describe it. Avebury Circles (of stones) are placed on an elevated 
plain of chalk, around which are elevated mounds or earthworks, the whole 
‘surrounded by a broad deep vallum, which is at all times perfectly dry, and it 


42 ‘“REPORT—1860. 


is on the driest and most exposed part of the mounds that the plant occurs. 
Its change from such a poor position to our garden, which though only un- 
manured forest marble-clay, is yet moist and stiff, will doubtless account for 
its wonderful growth. 

Cuscuta epilinum.—Our last year’s report on experiments in the growth 
of this Dodder excited so much attention, that we determined upon following 
out some additional ones in the present season, to which end we sowed two 
plots with flax-seed, as follows :— 

Plot 1. Flax-seed perfectly pure—The result was a very fine crop, per- 
fectly clean. 

Plot 2. Dirty Flax-seed with some seeds of Cuscuta epilinum infermixed.— 
This was scarcely half a crop, and the fine specimens of Dodder bearing 
down the partial crop, is at once an evidence of the mischief this parasite 
can do to the crop in question, as also of the perfect ease with which we can 
grow it ; so also how easy to prevent its presence in the flax-crop if we take 
care to sow pure seed. 

As regards the Clover Dodder, though this pest is yearly becoming more 
and more prevalent, yet this season has been especially bad for ripening its 
seed, and we are still in want of seed for special experiments upon it. 

Seeds of Orobanche minor have been collected this year with a view to a 
series of experiments upon it, as the Broomrape, like the Dodder, is yearly 
becoming more and more troublesome; and it would seem that Clovers are 
liable to attacks from both forms of the parasite, and in all probability of 
more than a single species of either; for, as regards Broomrape, we have col- 
lected the two forms O. minor and O. elatior from different Clover crops ; we 
still want to know whether the Cuscuta europea and C. Trifolit are specific- 
ally distinct. 

Myosotis —We last year reported upon some curious changes wrought in 
the cultivation of M. sylvatica, in which we gave it as an opinion that the 
M. palustris of authors was subject to great variations, giving rise to annual 
as well as perennial forms, the former introducing us to the M. sylvatica and 
others, as offsprings of M. palustris. Our present stock still bears out this 
view, as we have as derivatives from MW. sylvatica a still decreasing flowered 
form and annual and perennial conditions of our varieties. 

This year we introduced into the garden the very bright blue Forget-me- 
not of our ditches ; this in cultivation (the same plant) has become the small 
flowered light blue form which we take to be the M. repens of Don, as de- 
scribed by Mr. Babington. 

While upon this subject we must not omit to mention that, having been 
favoured with a packet of seed from the eminent firm of J. Carter and Co. of 
Holborn, under the name of Myosotis azurea major, we were much inter- 
ested in observing what kind of bedding plant it might make, particularly as 
in the Seed Catalogue for February 1860 we find the following remarks 
appended to the Myosotis species :— 

** Forget-me-not. These beautiful flowers are too well known to need 
recommendation : will grow around fountains, over damp rockeries, or in any 
moist situation. MM. azorica and azurea major are the finest.” 

Of course, from this announcement we expected something rather choice ; 
but our disappointment may be guessed when we found the result to be a 
very poor small light-coloured variety of MZ. palustris. 

Now, we are far from blaming the Messrs. Carter for this, as it will at once 
be seen that this was an induced form, and no one can at all answer for its 
permanency ; aud it may be that our position or some new circumstances of 

cultivation induced the change from an expected fine flower to a very insig- 


BALLOON COMMITTEE. 43 


nificant one. Still this affords another curious instance of the effects of cul- 
tivation upon this genus, which seem to tell us that we must not be too posi- 
tive in the specific distinctions adopted by authors for these plants. 


The effects of the season of 1860 have been remarkable in several particu- 
lars; we would, however, only refer to a few plants under experiment. 

Dioscorea Batatas, Potato Yam.—Smaller than ever; cannot be at all de- 
pended upon, even to make its seed in the Cotteswold district. 

The Cabbage tribe sadly cut up with us, but the Brussels Sprout was found 
to be the most hardy of any kind. 

Gyneria argentea.—Killed entirely, both in the College and our own 
private garden. 

Sorghum saccharatum.—Scarcely attained 6 inches in height against 7 feet 
of the previous year. 

Zea Mays.—Indian corn not 2 feet high, and died as soon as flowered. 

Roots of all kinds smaller than usual. 

Potatoes small in quantity and much diseased. 

Fruits have not attained their usual size, have not ripened, and are 
flavourless. 

Forest trees have made little wood, and their new shoots are not ripened. 

Garden flowers made little growth, shabby both in leaves and flowers. 

Plants perfected for less seed than usual. 

Cirencester, November, 1860. 


Report of the Committee requested “to report to the Meeting at 
Oxford as to the Scientific Objects to be sought for by continuing 
the Balloon Ascents formerly undertaken to great Altitudes.” By 
the Rev. Ropert Waker, M.A., F.R.S., Reader in Experimental 
Philosophy in the University of Oxford. 


{wn presenting their Report, the Committee would observe at the outset that 
the main object for which the former Committee (in 1858) was appointed 
remains yet unaccomplished ; and this is the verification of that remarkable 
result derived from the observations of Mr. Welsh in his four ascents in 
1852, viz. “the sudden arrest of the decrease in the temperature of the 
atmosphere at an elevation varying on different days, and this to such an 
extent, that for the space of 2000 or 3000 feet the temperature remains nearly 
constant or even increases to a small amount.” It is obviously important to 
determine whether this arrest represents the normal condition of the atmo- 
sphere at all seasons of the year. The ascents of Mr. Welsh were made 
between the 17th of August and the 10th of November. The question 
remains, whether this “arrest ” would be observed before the summer solstice 
as well as after, and whether there were any variations at different seasons. 
The changes in the temperature of the dew-point, consequent upon this in- 
terruption in the law of decrease of temperature, would extend our know- 
ledge of the condition of the atmosphere at such altitudes. To accomplish 
thus much would not require ascents to very great altitudes, although there 
are many objects to be attained by ascending as high as possible. The 
liberal offers that have been made by Mr. Coxwell and Mr. Langley, of New- 
castle, would enable observations to be made at a very moderate cost, and 
Mr. Langley appears fully competent to accomplish the task. There are 
also many other observations which may be made in balloon ascents which 


44 . REPORT—1860. 


may prove of very great value. Prof. W. Thomson is anxious that obser- 
vations should be made on the electrical condition of the atmosphere. He 
has described in the article on the Electricity of the Atmosphere in Nichol’s 
‘Cyclopedia,’ a portable electrometer, and also a mode of collecting electricity 
by that which he styles the water-dropping system, which would, in his 
opinion, be easily applicable. The observations might be carried on, first, 
by ascending to very moderate heights, and then going as high as possible. 
Dr. Lloyd desires that observations should be made for “the determination 
of the decrease of the earth’s magnetic force with the distance from the sur- 
face.” The failure of Gay-Lussac to detect any sensible change ought not 
to deter future observers. His methods were wholly inadequate; but Dr. 
Lloyd is of opinion that if attention be confined to the determination of the 
total force or its vertical component (instead of the horizontal), it would be 
easy to arrive at satisfactory conclusions. Sir David Brewster suggests that 
further information may be obtained as to the polarization of the atmosphere 
and the height of the neutral point. And, lastly, Dr. Edward Smith and 
Prof. Sharpey are desirous that experiments should be made as to “the 
quantitative determination of the products of respiration at different high 
elevations.” Dr. Smith has, as it is well known, been for the last two or 
three years engaged in experimental inquiries on inspiration, and he is so 
satisfied of the value and importance of the investigation, that he is not only 
willing, but desirous to make the requisite experiments himself. Dr. Smith 
has furnished directions as to the points to be observed and the mode of ob- 
servation. 


Report of Committee appointed to prepare a Self-Recording Atmo- 
spheric Electrometer for Kew, and Portable Apparatus for observing 
Atmospheric Electricity. By Professor W. Tuomson, F.R.S. 


Your Committee, acting according to your instructions, applied to the Royal 
Society for £100 out of the Government grant for scientific investigation, to 
be applied to the above-mentioned objects. This application was acceded 
to, and the construction of the apparatus was proceeded with. The progress 
was necessarily slow, in consequence of the numerous experiments required 
to find convenient plans for the different instruments and arrangements to 
be made. An improved portable electrometer was first completed, and is 
now in a form which it is confidently hoped will be found convenient for 
general use by travellers, and for electrical observation from balloons. A 
house electrometer, on a similar plan, but of greater sensibility and accuracy, 
was also constructed. Three instruments of this kind have been made, one 
of which (imperfect, but sufficiently convenient and exact for ordinary work) 
‘is now in constant use for atmospheric observation in the laboratory of the 
Natural Philosophy Class in the University of Glasgow. The two others are 
considerably improved, and promise great ease, accuracy, and sensibility 
for’ atmospheric observation, and for a large variety of electrometric re- 
searches. Many trials of the water-dropping collector, described at the last 
Meeting of the Association, were also made, and convenient practical forms - 
of the different parts of the apparatus have been planned and executed. A 
reflecting electrometer was last completed, in a working form, and, along 
with a water-dropping collector and one of the improved common house 
electrometers, was deposited at Kew onthe 19thof May. A piece of clock- 


EXPERIMENTS UPON WROUGHT-IRON GIRDERS. 45 


work, supplied by the Kew Committee, completes the apparatus required 
- for establishing the self-recording system, with the exception of the merely 
photographic part. It is hoped that this will be completed, under the 
direction of Mr. Stewart, and the observations of atmospheric electricity com- 
menced, in little more than a month from the present time. In the mean 
time preparations for observing the solar eclipse, and the construction of 
magnetic instruments for the Dutch Government, necessarily occupy the staff 
of the Observatory, to the exclusion of other undertakings. It is intended 
that the remaining one of the ordinary house electrometers, with a water- 
dropping collector, and the portable electrometer referred to above, will be 
used during the summer months for observation of atmospheric electricity in 
the Island of Arran. Your Committee were desirous of supplying portable 
apparatus to Prof. Everett, of Windsor, Nova Scotia, and to Mr. Sandiman, 
of the Colonial Observatory of Demerara, for the observation of atmospheric 
electricity in those localities; but it is not known whether the money which 
has been granted will suffice, after the expenses yet to be incurred in esta- 
blishing the apparatus at Kew shall have been defrayed. In conclusion, it is 
recommended to you for your consideration by your Committee, whether 
you will not immediately take steps to secure careful and extensive obser- 
vations in this most important and hitherto imperfectly investigated branch 
of meteorological science. For this purpose it is suggested,—1. that, if 
possible, funds should be provided to supply competent observers in different 
parts of the world with the apparatus necessary for making precise and com- 
parable observations in absolute measure; and 2. that before the con- 
clusion of the present summer a commencement of electrical observation 
from balloons should be made. 


Experiments to determine the Effect of Vibratory Action and long- 
continued Changes of Load upon Wrouyht-iron Girders. By 
WivuiaM Fairsairn, Ksq., LL.D., F.R.S. 


AMONGST engineers opinions are still much divided upon the question, whe- 
ther the continuous changes of load which many wrought-iron constructions 
undergo, has any permanent effect upon their ultimate powers of resistance ; 
that is, whether a beam or other construction subjected to a perpetual change 
of load, would suffer such an alteration in the structure of the iron or the 
tenacity of the joints, that it would in time break with a much less force than 
its original breaking weight. But few facts are known, and few experiments 
have been made bearing on the solution of this question. We know that in 
some cases wrought iron subjected to continuous vibration assumes a crystal- 
line structure, and is then deteriorated in its cohesive powers ; but we are yet 
very ignorant of the causes of this change, and of the precise conditions 
under which it occurs. 

A few experiments were made by the Commission appointed to inquire 
into the application of iron to railway structures, to ascertain the effect of 
changes of load upon homogeneous bars of wrought and cast iron. They 
found with cast iron that no bar would stand 4000 impacts, bending them 
through one-half of their ultimate deflection, but that sound bars would 


46 REPORT—1!860. 


sustain at least 4000 impacts, bending them through one-third of their ulti- 
mate statical deflection. They ascertained also, that when the load was 
placed upon the bars without impact, if the deflection did not exceed one- 
third of the ultimate deflection, the bar was not weakened ; but that if the 
deflection amounted to one-half the ultimate deflection, the bars were broken 
with not more than 900 changes of load. With wrought iron bars they 
found no perceptible effect from 10,000 changes of load, when the deflections 
were produced by a weight equal to half the statical breaking weight. 

These experiments are interesting so far as they go, but they are very in- 
complete as regards wrought iron. For wrought-iron bars they were not 
continued long enough, nor do they apply to those larger constructions in 
which the homogeneous bar is replaced by riveted plates. The influence 
of change of load on riveted constructions possesses a special importance, 
from its bearing on the question of the proper proportion of strength in 
plate and tubular bridges. Do these constructions gradually become weak- 
ened from the continual passage of trains? and is it requisite to make allow- 
ance for such a deterioration by increased sectional area of material] in their 
original construction? These questions I have sought to solve by the fol- 
lowing experiments. 

As the load is brought upon bridges in a gradual manner, the apparatus 
is designed to imitate as far as possible this condition. A riveted beam is 
fixed on brickwork supports, 20 feet apart. Beneath this is placed a lever 
grasping the lower web of the beam, and fastened upon a pivot at the ful- 
crum. At the other extremity it carries the scale and weights. This lever 
is lifted clear of the beam, and again lowered upon it by means of a connect- 
ing rod attached to one of the arms of a spur-wheel placed at a considerable 
distance overhead. In this way any required part of the breaking weight 
can be lifted off and replaced upon the beam alternately by the revolution of 
the spur-wheel. The apparatus is worked night and day by a water-wheel, 
and the number of changes of load is registered by a counter. 

The girder subjected to vibration in these experiments is a plate girder of 
20 feet clear span, and of the following dimensions :— 


Sq. in. 
Area of top: 1 plate, 4in.x}in......,.. Sine. | 200 
2 2 angle-irons, 2X2X 79; ........ 2°30 
—— 4°30 
Area of bottom: 1 plate, 4 in.x1tin........... 1°00 
35 2 angle-irons, 2x2x73...... 14 
—— 340 
Web, 1 plate 155% 4.2.5. sb ds shi. cate eees 1:90 
Total sectional area .............0005 ; 8°60 
Depth, s,i006 9 ts02 06 Steaebesiniaswcls 16 ins 
Weight : ~ab.)5.52 pase peep sass oiss)) TD eowk 3.qns; 


Breaking weight (calculated) Ba sipn. aipisy emai 


This beam having been loaded with 6643 lbs., equivalent to one-fourth of 
the ultimate breaking weight, the experiment commenced. 


EXPERIMENTS UPON WROUGHT-IRON GIRDERS. 47 


Tas e I.—Experiment on Wrought-iron Beam with a changing load 
equivalent to one-fourth of the breaking weight. 


Date, Number of Deflection 


1860. changes of load. | produced by load. Remarks. 
March 21 0 0°17 
» 22 10,540 0-18 
i 7 craints O16 Strap loose and failing to lift 
; SB Oe bille. eh wile 5 5 é 
26 46,100 0-16 the weigt: 
‘ania 57,790 0°17 
eSB 72,440 0-17 
oe 85,960 0°17 
25.30 97,420 0°17 
ey on 112,810 0°17 
April 2 144,350 0°16 
‘ae 165,710 0:18 
ee 202,890 0°17 
o10 235,811 0°17 
ee 268,328 0°17 
oe | | 281,210 0-17 
3 («17 321,015 0°17 
3° «20 343,880 0°17 Strap broken. 
pH rg 390,430 017 
#428 408,264 0-16 
io. 28 417,940 0°16 
May 1 449,280 0°16 
a. Se 468,600 0°16 
ee 489,769 0'16 
ae 512,181 0-16 
Bald 536,355 0°16 
ue 560,529 0°16 
5 14 596,790 0°16 


As the beam had now undergone above half a million changes of load, 
that is, it had worked continuously for two months, night and day, at the 
rate of about eight changes per minute, and as it had undergone no visible 
alteration, the load was increased from one-fourth to two-sevenths of the 
statical breaking weight, and the experiment proceeded with till the number 
of changes of load reached a million. 


Tasxe IJ.—Experiment on the same Beam with a load equivalent to two- 
sevenths of the breaking weight, or nearly 33 tons. 


Date, Number of Deflection 


1860. changes of load. in inches. Remarks. 

May 14 0 0-22 In this Table the number of 
i elo 12,623 0°22 changes of load are counted 
me ay 36,417 0°22 from 0, although the beam had — 
, 19 53,770 0°21 j already undergone 596,790 
a 22 85,820 0°22 changes, as shown in the pre- 
» 26 128,300 0°22 ceding Table. 

» 29 161,500 0°22 
» 31 177,000 0-22 

June 4 194,500 0°21 
mt fF 217,300 0°21 
e 9 236,460 0-21 
s 12 264,220 0-21 
» 16 292,600 0°22 
m. 20 403,210 0:23 The beam had now suffered a 


million changes of load. 


48 REPORT—1860. 


TaBLeE IJI.—Experiment on the same Beam with a load equivalent to 
two-fifths of the breaking weight. 


Date, Number of Deflection 


1860. changes of load. in inches. Remarks, 


June 2 


7 0 
Sy 2S 5175 


The beam broke after 5175 changes with aload equivalent to two-fifths of 
the breaking weight, although with lesser weights it had appeared uninjured. 


Summary of Results. 


Ratio of load | Number of | Total number aes 
Table. | to breaking | changes with | of changes of een me Remarks. 
weight. each load. load. 
16 1:40 596,790 596,790 0-17 
10F 1:34 403,210 1,000,000 0:22 
III. 1:2°5 5,175 1,005,175 0:35 Broke. 


Since these experiments were made the beam has been repaired, and has 
made 1,500,000 additional changes with a load equivalent to one-fourth of the 
breaking weight without giving way. It would appear, therefore, that with a 
load of this magnitude the structure undergoes no deterioration in its molecular 
structure ; and provided a sufficient margin of strength is given, say from five 
to six times the working load, there is every reason to believe, from the results 
of the above experiments, that girders composed of good material and of 
sound workmanship are indestructible so far as regards mere vibratory action. 

As the experiments on this important subject are still in progress, we hope 
to bring the subject more in detail before the Association at its next Meeting. 


A Catalogue ¢f Meteorites and Fireballs, from a.p. 2 to A.D. 1860. 
By R. P. Gree, Esq., F.G.S. 


1. Turs Catalogue is intended partly as a sequel to the Reports on Lumi- 
nous Meteors, now continued for a series of years in the volumes of the British 
Association Reports, and partly as a continuation, in a corrected and extended 
form, of a Catalogue of Meteorites published by the author, in two papers 
on the same subject, in the Numbers of the Philosophical Magazine and 
Journal of Science for November and December 1854. 

2. The following works and periodicals have been consulted, viz—Thom- 
son's Meteorology, 1849; Transactions of the Royal Society ; Nicholson's 
Journal of Natural Philosophy ; Thomson’s Annals of Philosophy ; London, 
Edinburgh, and Dublin Philosophical Magazine; Brewster's Encyclopedia, 
article “ Meteorite ;” Annual Register; Journal of the Asiatic Society of 
Bengal; British Association Reports; Proceedings of the Royal Irish 
Academy ; Spurgeon’s Annals of Electricity ; New Edinburgh Philosophical 
Journal ; Partsch’s, Shepard’s, and Reichenbach’s Catalogues of Meteorites ; 
R. Wolf’s, Chladni’s, Boguslawski’s, Quetelet’s, Baumhauer's, and Coulvier- 
Gravier’s Catalogues ; Dr. Clark’s Thesis on Iron Meteoric Masses ; Poggen- 
dorff’s Annalen; Annales de Chimie et de Physique; Comptes Rendus; Trans- 
actions of the Imperial Academy of Arts and Sciences of Vienna, 1859-60, 
papers by W. Haidinger; Transactions of the Royal Academy of Brussels ; 
Quarterly Journals of the Natural History Society of Zurich, 1856; Die 
Feuermeteore insbesondere die Meteoriten, &c., von Dr. Otto Buchner of 


CATALOGUE OF METEORITES AND FIREBALLS, 49 


Giessen, 1859; Lithologia meteorica del Profesor Joaquin Balcells, Barce- 
lona, 1854; Report on Meteorites, by Prof. Shepard; Reports of the Smith- 
sonian Institution, United States; Silliman’s American Journal ; as well as 
various private notices and public journals. I have likewise to acknowledge 
the kind assistance and valuable information received from Herr P. A. Kessel- 
meyer, Dr. Buchner, Herr W. von Haidinger, and Professor Heis. 

3. The few abbreviations used in this Catalogue speak for themselves, and 
hardly need explanation. Where weights of meteorites are stated, it is gene- 
rally intended to denominate lbs. Troy, English, though sometimes the Vienna 
or Prussian pound has unavoidably been given. Tables of analysis are added 
at the end of the catalogues. Genuine cases of stone- or iron-falls and de- 
tonating meteors, are marked with an asterisk (*), and in the Tables count 
for 1; doubtful cases are marked in the Catalogue with a (?), and count as 4 
in the Tables. 

The numbers in some of the Tables, it will be found, do not quite agree 
with those in the corresponding Tables given in the Report on Luminous 
Meteors, in the Volume of the British Association Reports for 1860, owing 
to the circumstance that when that Report was presented at the Oxford Meet- 
ing the present Catalogue was not then quite completed. 

4. A few remarks are added to the Tables, which do not eall for much 
comment in this place, as they have mostly already been alluded to in the 
aforesaid Report. With regard to the November period for shooting stars, 
E. C. Herrick, of the United States, considers it to be advancing into the 
year; in A.p. 1202, it occurred about the 26th October; in 1366 on October 
30th ; so that the motion of the node of the zone or ring which furnishes 
these shooting stars, is at the rate of 3 or 4 days a century ; the period itself 
being a recurrent one probably of about 33 years. (See Silliman’s Journal, 
No. 91, p. 137, for January 1861.) 

5. In the Catalogue itself great care has been taken in separating the dif- 
ferent kinds of fireballs and aérolites; hitherto this has not been done with 
sufficient care, and large meteors have not unfrequently been called aérolitic, 
when not even any detonation has been reported; examples of this not 
unfrequently occur in the catalogues of Baumhauer, Kamtz, and Arago. 
Dr. Buchner of Giessen, and P. A. Kesse!meyer of Frankfort-on-Maine, will, 
I understand, shortly bring out catalogues of aérolitic falls, where details 
in matters concerning original authorities and geographical distribution, &c. 
will be given very fully. 

In the Tables at the end of this Catalogue, Class A includes only cases 
where stones or irons have really fallen; Class B, meteors accompanied by 
detonation ; Class C, first-class meteors mot accompanied by detonation ; this 
class includes all fireballs given in the catalogues up to the year 1820; after 
that time, only the most remarkable ones, as in consequence of the subsequent 
greatly increased number of observations from about that time, it is evident 
the described fireballs would probably be of smaller size than for older ob- 
servations ; Class D includes all fireballs mentioned in the catalogues and 
supplements, large or small, where no detonation was reported, and of course 
includes the C class. The Tables are so cunstructed, that a glance will suffice 
to show the results as regards numbers and dates, and the proportion which 
one class bears to another; some of them will be found to be not without 
some interest. 


Note—— Wherever the words “ Stone-fall” or “ Irou-fall” occur, it may be 
understood, as a rule, that such phenomenon was also accompanied by a 


detonating fireball, or at least by a detonation. 
1860. E 


REPORT—1860. 


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1860. 


REPORT 


56 


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110 


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CATALOGUE OF METEORITES AND FIREBALLS. 119 


REMARKS. 


1. While there appear to be eight yearly maximum and minimum aérolitic 
periods for the years generally, there are likewise some indications of other 
periods for some of the months taken separately. 

Some months may have major or longer periods of maximum, as Novem- 
ber, which perhaps has one of about 70 years (though for the sporadic 
showers, according to Herrick, one of 33 years, in which case the numbers 
of shooting stars should now be again on the increase, so as to culminate in 
1866). January has also probably a long or irregular period, as regards 
classes A and B. Of late years the numbers for December and January 
have evidently been on the increase, and especially as regards the former 
month, and this as regards all classes ; and the eighth to the seventeenth days 
appears to embrace a time favourable to a considerable increase over the 
average for the month. Tables I., II., II., and IV. § 

2. The proportionate numbers of each class appear to have varied at dif- 
ferent times for the different months. Table VIII. 

3. There appear to be aérolitic and meteor epochs both distinct from and 
common to each other. A proximate attempt has been made to show some 
of these in Table V.; perhaps some of these are more apparent than real; 
but the subject is worth consideration. 

4. While the aérolitic class, A and B, in its total is under the average for 
August, which is the principal and most constant month for an abundance of 
sporadic meteors, it is over the average for November, likewise a month 
noted for an abundant display of meteors and shooting stars ; and while there 
is an increase over the average of detonating meteors (though not of recorded 
Stone-falls), from the 9th to the 13th of November, i. e. precisely during the 
regular periodical appearance, it is uota little singular that the August aéro- 
litie period, if it may be so called, precedes by several days the usual period 
of greatest abundance of the shooting stars ; one being August 4 to 7, both 
inclusive, and the other August 9 to 12. See Table III. 

5. The decided preponderance of aérolitic phenomena, alluded to in the 
Report as occurring in the afternoon, as compared with the forenoon, will 
be seen clearly given in Table IX. 

6. As regards the observed direction of aérolitic and first-class meteors, 
there would seem not to be any very great tendency one way or the other ; 
it would have been natural to have expected a much more decided leaning to 
a Westerly direction. The sudden change from an Easterly direction in Sep- 
tember and October (about the time of the autumnal equinox), toa Westerly 
direction in November, is remarkable, and calls for especial notice. 

7. The considerable increase of aérolitic falls and meteors for the months 
of June and July over those of December and January has been previously 
alluded to in the Report itself. That more detonating meteors in proportion 
to Stone-falls should be recorded during the winter months than during the 
summer months, is precisely what might have been expected, and the reverse 
holds equally good. Tables VI. and VII. 

8. Taking the entire year, there is a much greater tendency towards equality 
of distribution in the aérolitic class than is the case with sporadic shooting stars 
and the smaller meteors; indeed, were it not for the excess in November (an 
excess common to every class apparently), the numbers of the former (Aand 
B) would be about equal for the first as for the second half of the year. 


120 REPORT—1860. 


CORRIGENDA ET ADDENDA. 


Page 53, line 22 from top: for “1596” read 1596.x. 

Page 59, line 18 from top: for “ Sarthé” read Sarthe. 

Page 62, 1804. Apr. 15. Geneva. fireball: add, s.to N.; also, followed by a train of smaller 
balls. 

Page 64, line 18 from top: for “ Aug. 10” read early part of Aug. 

Page 64, line 12 from bottom : for “ Iron-fail” read Stone-fall. 

Page 65, line 7 from bottom: fireball at Gottingen; add, followed by many smaller balls. 

Page 67, top line: for “1819. June 13. Jonsac’”’ read and add, 1819.x June 13. Jonsac, 
Charente, &c. &e. 

Page 70, line 5 from top: Gorlitz; fireball; add aérolitic ?. 

Page 71, line 11 from bottom: replace the (x) before May 12, by a (?). 

Page 71, line 12 from bottom: insert the (x) before May 19. Ekaterinosloff, &c. 

Page 72, line 6 from top: read February 27 or February 16. 

Page 72, line 11 from bottom of Notes: for “‘ Summer co.’’ read Sumner co. 

Page 73, line 3 fron top: add Vouillé near “ Poitiers.” 

Page 74, line 21 from top: for ‘ Okaninak ” read Okaninah. 

Page 82, line 6 from top: for ‘‘ Nuremberg ” read Nurenberg. 

Page 92, after line 5 from top: insert, Apr. 12. Berne. Fireball. 

Page 94, line 10 from top : for “ Columb ” read Columbus. 

Page 96, after line 16 from bottom: insert 1860.x Feb. 2. Alessandria, Piedmont. A stone- 
fall, Also omitted in the Tables. 


Report on the Theory of Numbers.—Part Il. By H. J. SrepnHen 
Smitu, M.A., F.R.S., Savilian Professor of Geometry, Oxford. 


39. Residues of the Higher Powers. Researches of Jacobi.—The principles 
which have sufficed for the determination of the laws of reciprocity affecting 
quadratic, cubic, biquadratic, and sextic residues, are found to be inadequate 
when we come to residues of the 5th, 7th, or higher powers. This was early 
observed by Jacobi, when, after his investigations of the eubie and biqua- 
dratic theorems, he turned his attention to residues of the 5th, 8th, and 12th 
powers*. It was evident, from a comparison of the cubic and biquadratic 
theories, that in the investigation of the laws of reciprocity the ordinary 
prime numbers of arithmetic must be replaced by certain factors of those 
prime numbers composed of roots of unity ; and Jacobi, in the note just re- 
ferred to, has indicated very clearly the nature of those factors in the case 
of the 5th, 8th, and 12th powers respectively. He ascertained that the two 
complex factors composed of 5th roots of unity into which every prime 
number of the form 5z+1 is resoluble by virtue of Theorem LV. of art. 30 
of this Report, are not prime numbers, i. e. are each capable of decomposi- 
tion into the product of two similar complex numbers; so that every (real) 
prime number of the form 5x+1 is to be regarded as the product of four 
conjugate complex factors ; and these factors are precisely the complex primes 
which we have to consider in the theory of ‘quintic residues, in the place of 
the real primes they divide. ‘To this we may add that primes of the forms 
5n+2 continue primes in the complex theory; while those of the form 52—1 
resolve themselves into éwo complex prime factors. Thus 


7=7; 1l=(2+a)(2+0°)(2+a*)\(2+a'); 13=13; 
19=(4—3(a+a*))(4—3(a?+2°)); 29=(5—(a+a'))(5—(a?+a°)) ; 
31=(2—2a)(2—2°)(2—a*)(2—a'), &e., 


* See a note communicated by him to the Berlin Academy on May 16, 1839, in the 
‘Monatsberichte’ for that year, or in Crelle, vol. xix. p. 314, or Liouville, vol. viii. p. 268, 
in which, however, he implies that he had not as yet obtained a definitive result; nor does 
he seem at any subsequent period to have succeeded in completing this investigation. 


q 


ON THE THEORY OF NUMBERS. 121 


where @ is an imaginary 5th root of unity. Precisely similar remarks apply 
to the theories of residues of 8th and 12th powers,—real primes of the forms 
8u+1, 12”+1, resclving themselves into four factors composed of Sth and 
12th roots of unity respectively. By considerations similar to those pre- 
viously employed by him in the case of biquadratic and cubic residues, 
Jacobi succeeded in demonstrating (thorgh he has not enunciated) the for- 
mul of reciprocity affecting those powers for the particular case in which 
one of the two primes compared is a real number. But it would seem that 
he never obtained the law of reciprocity for the general case of any two 
complex primes; and indeed, for a reason which will afterwards appear, it 
was hardly possible that he should do so, so long as he confined himself to 
the consideration of those complex numbers which present themselves in the 
theory of the division of the circle. No less unsuccessful were the efforts of 
Eisenstein to obtain the formule relating to 8th powers, by an extension of 
the elliptical properties employed by him in his later proofs of the biqua- 
dratic theorem *. It does not appear that any subsequent writer has occu- 
pied himself with these special theories ; while, on the other hand, the theory 
of complex numbers composed with roots of unity of which the exponent is 
any prime, has been the subject of an important series of investigations by 
MM. Dirichlet and Kummer, and has led the latter eminent mathematician 
to the discovery and demonstration of the law of reciprocity, which holds for 
all powers of which the exponent is a prime number not included in a cer- 
tain exceptional class. 

40. Necessity for the Introduction of Ideal Primes.—The fundamental pro- 
position of ordinary arithmetic, that if two numbers have each of them no 
common divisor with a third number, their product has no common divisor 
with that third number, is, as we have seen, applicable to complex num- 
bers formed with 3rd or 4th roots of unity, because it is demonstrable that 
Euclid’s theory of the greatest common divisor is applicable in each of those 
cases. With complex numbers of higher orders this is no longer the case ; 
and it is accordingly found that the arithmetical consequences of Euclid’s 
process, which are of so much importance in the simpler cases, cease to exist 
in the general theory. In particular, the elementary theorem, that a number 
can be decomposed into prime factors in one way only, ceases to exist for 
complex numbers composed of 23rd + or higher roots of unity—if, at least 
(in the case of complex as of real numbers), we understand by a prime fac- 
tor, a factor which cannot itself be decomposed into simpler factors}. It 
appears, therefore, that in the higher complex theories, a number is not 
necessarily a prime number simply because it cannot be resolved into com- 
plex factors. But by the introduction of a new arithmetical conception— 
that of ideal prime factors—M. Kummer has shown that the analogy with 
the arithmetic of common numbers is completely restored. Some prelimi- 
nary observations are, however, necessary to explain clearly in what this con- 
ception consists. 


* See M. Kummer, “ Ucber die Allgemeinen Reciprocitiatsgesetze,” p. 27, in the Memoirs 
of the Berlin Academy for 1859. 

ft For complex numbers composed with 5th or 7th roots of unity, the theorem still exists ; 
for 23 and higher primes it certainly fails; whether ‘it exists or not for 11, 13, 17, and 19, 
has not been definitely stated by M. Kummer (see below, Art. 50). 

~ “Maxime dolendum videtur” (so said M. Kummer in 1844) “quod hee numerorum 
realium virtus, ut in factores primos dissolvi possint, qui pro eodem numero semper iidem 
sint, non eadem est numerorum complexorum, que si esset, tota hiec doctrina, que magnis 
adhue difficultatibus premitur, facile absolvi et ad finem perduci posset.” (See his Disserta- 
tion in Liouville’s Journal, vol. xii. p. 202.) In the following year he was already able to 
withdraw this expression of regret. 


122 REPORT—1860. 


41. Elementary Definitions relating to Complex Numbers.—Let ) be a prime 


a 
2 ark : 

number, and @ a root of the equation 2a =0; then any expression of the 
form 

F(a)=a,+a,a+4,0°+....+a,_,0*-” were en 

in which a@,, a,, @,,.+--+@,_., denote real integers, is called a complex inte- 

gral number. To this form every rational and integral function of @ can 

always be reduced; and it follows, from the irreducibility of the equation 

nal “ : 

ae tages that the same complex number cannot be expressed in this 

reduced form in two different ways. The zorm otf F(a) is the real integer 

obtained by forming the product of all the A—1 values of F(a), so that 


N.F(a)=N.F(a*)=... =N. F(a*—!)=F(a). F(a). F(a")... F(a*-!). 


The operations of addition, subtraction and multiplication present no pecu- 
liarity in the case of these complex numbers; by the introduction of the 
norm, the division of one complex number by another is reduced to the case 
in which the divisor is a real integer. Thus 


fa) _flayE()E(a’)-...F(@) | 

F(a) N.F(a) ; 
and f(a) is said to be divisible by F(a) when every coefficient in the pro- 
duct f(a)F(a*)F(a’)...F(a*—!), developed and reduced to the form (A), 
is divisible by N. F(a). When f(a) is not divisible by F(a), it is not, in 
general, possible to render the norm of the remainder less than the norm of 
the divisor; and it is owing to this circumstance that the common rule for 
finding the greatest common divisor is not generally applicable to complex 
numbers. If, in the expression (A), we consider the numbers a,, @,.--@,—2 
as indeterminates, the norm is a certain homogeneous function of order \—1, 
and of A—1 indeterminates; so that the inquiry whether a given real number 
is or is not resoluble into the product of \—1 conjugate complex factors, is 
identical with the inquiry whether it is or is not capable of representation by 
a certain homogeneous form, which is, in fact, the resultant of the two forms 


O44 77+ 4,07 Sy 4 +°:° +Gy2y?—*, 
and age 9 oo aR! i al ah tin 


The problem is considered in the former aspect by M. Kummer, in the latter 
by Dirichlet. The methods of Dirichlet appear to have been of extreme 
generality, and are as applicable to complex numbers, composed with the 
powers of a root of any irreducible equation having integral coefficients, as 
to the complex numbers which we have to consider here. Nevertheless, in 
the outline of this theory which we propose to give, we prefer to follow the 
course taken by M. Kummer: for Dirichlet’s results have been indicated 
by him, for the most part, only in a very summary manner *; nor is it in any 
case difficult to assign to them their proper place in M. Kummer’s theory ; 
while, on the other hand, it would, perhaps, be impossible to express ade- 
quately, in any other form than that which M. Kummer has adopted, the 
numerous and important results (including the law of reciprocity itself) con- 


* See his notes in the Monatsberichte of the Berlin Academy for 1841, Oct. 11, p. 280; 
1842, April 14, p. 93; and 1846, March 30; also a letter to M. Liouville, in Liouville’s 
Journal, vol. v. p. 72; a note in the Comptes Rendus of the Paris Academy for 1840, 
vol. x. p. 286; and another in the Monatsberichte for 1847, April 15, p. 139, 


ON THE THEORY OF NUMBERS, 123 


tained in the elaborate series of memoirs which he has devoted to this sub- 
ject *. 

42. Complex Units——A complex unit is a complex number of which the 
norm is unity. If \=3, there is only a finite number [six] of units included 
in the formula +a". But for all higher values of X, the number of units is 
infinite. Nevertheless it is always possible to assign a system of »—1 units 
(putting, for brevity, 3(A—1)=,) such that ad/ units are included in the 
formula tatu ....u ts"; in which w,, t@,, Ws)+++%,—1 are the assigned 
units, and f, 7,, 2,,..-2,—1, are real (positive or negative) integral numbers. 
A system of units, capable of thus representing all units whatsoever, is called 
a fundamental system. The existence, for every value of A, of fundamental 


* The following is a list of M. Kummer’s memoirs on complex numbers :— 

1, De numeris complexis qui radicibus unitatis et numeris realibus constant, Breslau, 
1844. This is an academical dissertation, addressed by the University of Breslau to that of 
Konigsberg, on the tercentenary anniversary of the latter. It has been inserted by M. Liou- 
ville in his Journal, vol. xii. p. 185. 

2. Ueber die Divisoren gewisser Formen der Zahlen, welche aus der Theorie der Kreis- 
theilung entstehen.—Crelle, vol. xxx. p. 107. 

3. Zur Theorie der Complexen Zahlen, in the Monatsberichte for March 1845, or in 
Crelle, vol. xxxv. p. 319. 

4. Ueber die Zerlegung der aus Wurzeln der Einheit gebildeten complexen Zahlen in ihre 
Primfactoren.—Creille, vol. xxxv. p. 327. The date is Sept. 1846. 

5. A note addressed to M. Liouville (April 28, 1847), in Liouville’s Journal, vol. xii. p. 136. 

6. Bestimmung der Anzahl nicht zquivalenter Klassen fiir die aus Aten Wurzeln der Ein- 
heit gebildeten complexen Zahlen, und die idealen Factoren derselben.—Crelle, vol. xl. p. 93. 

7. Zwei besondere Untersuchungen iiber die Classen-Anzahl, und iiber die Einheiten der 
aus Aten Wurzeln der Einheit gebildeten complexen Zahlen.—Crelle, vol. x1. p- 117. (See 
also the Monatsberichte of the Berlin Academy for 1847, Oct. 14, p. 305.) 

8. Allgemeiner Beweis des Fermat’schen Satzes, dass die Gleichung 2*+-y%=7zA unlésbar 
ist, fiir alle diejenigen Potenz-Exponenten A, welche ungerade Primzahlen sind, und in den 
Zahlern der ersten 3(\—3) Bernouillischen Zahlen als Factoren nicht vorkommen.—Crelle, 
vol. xl. p.131. (See also the Monatsberichte for 1847, April 15, p.132.) This and the two 
preceding memoirs are dated June 1849. 

9. Recherches sur les Nombres Complexes.—Liouville, vol. xvi. p. 377. This memoir 
contains a very full résumé of the whole theory, and may be read by any one acquainted 
with the elements of the theory of numbers. 

10. A note in the Monatsberichte of the Berlin Academy for May 27,1850, p. 154, which 
contains the first enunciation of the law of reciprocity. 

11. Ueber die Erganzungssitze zu den Allgemeinen Reciprocitatsgesetzen.—Crelle, vol. xliv. 
p- 93 (Nov. 30, 1851), and vol. lvi. p. 270 (Dec. 1858). 

12, A note on the irregularity of determinants, in the Berlin Monatsberichte for 1853, 
March 14, p. 194, 

13, Ueber eine besondere Art aus complexen Einheiten gebildeter Ausdriicke.—Crelle, 
vol. l. p. 212 (Aug, 31, 1854). 

14. Ueber die den Gaussischen Perioden der Kreistheilung entsprechenden Congruenz- 
wurzeln.—Crelle, vol. liii. p. 142 (June 5, 1856). 

15. Einige Satze tiber die aus den Wurzeln der Gleichung aA =1 gebildeten complexen 
Zahlen fiir den Fall, dass die Klassenzahl durch A theilbar ist, nebst Anwendung derselben 
auf einen weiteren Beweis des letzten Fermat’schen Lehrsatzes.—Memoirs of the Berlin 
Academy for 1857, p.41. An abstract of this memoir will be found in the Monatsberichte 
for 1857, May 4, p. 275. 

16. Theorie der Idealen Primfactoren der complexen Zahlen, welche aus den Wurzeln 
der Gleichung w”=1 gebildet sind, wenn n eine zusammengesetzte Zahl ist.—Memoirs of the 
Berlin Academy for 1856, p. 1. 

17. Ueber die Allgemeinen Reciprocitatsgesetze unter den Resten und Nicht-Resten der 
Potenzen, deren Grad eine Primzahl ist—Memoirs of the Berlin Academy for 1859, p. 20. 
Tt was read on Feb. 18, 1858, and May 5, 1859. An abstract will be found in the Monats- 
berichte of the former year. 

A memoir by M. Kronecker (De unitatibus complexis, Berlin, 1845; it is his inaugural dis- 
sertation on taking his doctorate) connects itself naturally with the earlier memoirs of the 
preceding series. : 


124 REPORT—1860. 


systems of »—1 units may be established by means of a general proposition 
due to Dirichlet and relating to any irreducible equation having unity for 
its first coefficient, and all its coefficients integral. If, in such an equation, 
R be the number of real, and 2I of imaginary roots, there always exist 
systems of R+I—1 fundamental units, by means of which all other units 
can be expressed; or, in other words, the indeterminate equation “Norm 
=1” is always resoluble in an infinite number of ways, and all its solutions 
can be expressed by means of R+I—1 fundamental solutions*. The demon- 
stration of the actuai existence, in every case, of these systems of fundamental 
units (a theorem which is, as Jacobi has said+, “un des plus importants, 
mais aussi un des plus épineux de la science des nombres”) is of essential im- 
portance in the theory of complex numbers, and has the same relation to 
that theory which the solution of the Pellian equation 2*—Dy’=1 has to 
the theory of quadratic forms of determinant D. It may be observed, how- 
ever, that in the case which we have to consider here, that of the equation 
a 
= 7 =o the existence of fundamental systems of »—1 units has been 


a= 
demonstrated independently of Dirichlet’s general theory by MM. Kro- 
necker and Kummerf. 
If A=5, a+a-! is the only fundamental unit; so that every unit is in- 
cluded in the formula 
ta*(a+a-1)”. 


If \=7, the complex units are included in the formula 
ta* (atta) (a? +a), 


But for higher primes the actual calculation of a system of fundamental units 
involves great labour; and a method practically available for the purpose 
has not yet been given. It is remarkable that every unit can be rendered 


real (i. e. a function of the binary sums or periods a'+a—", &c.) by multi- 
plying it by a properly assumed power of a. We shall therefore suppose, in 


* To enunciate Dirichlet’s theorem with precision, let f(v)=0 be the proposed equation ; 
let 1, @g)+.. a» be its roots, and y(a,), (#,),..- P(#n) a system of n conjugate units. If 
the analytical modulus of every one of the quantities Y(«;), W(a2),...W(#,) be unity, the 
system of units is an isolated or singular system. The number of singular systems (if any 
such exist) is always finite, whence it is easy to infer that the units they comprise are 
simply roots of unity. For if ~(«) be a singular unit, its powers are evidently also singular 
units, and therefore cannot be all different from one another; 7. e. /(«) is a root of unity. 
If f(x) be of an uneven order, there are no singular units; if f(a) be of an even order, —1 
is a singular unit; and if /(a)=0 have any real roots, it is the only singular unit; whereas 
if all the roots of f(a#)=0 be imaginary, other singular units may in special cases exist. 

A 
tae 

nO =0 has 2(A—1) singular units included in the formula +e*, Ad- 
mitting this definition of singular units, we may enunciate Dirichlet’s theorem as follows :— 
a system of A units [A=I+R—1], e,(a), eo(),...ex(@), composed with any root #, can 
always be assigned such that every unit composed with the same root can be represented 
(and in one way only) by the formula 


w .€y(a)"1. €5(a)"2, @,(c)"3.... en()"A, 


where 7, 7%)... 7, are positive or negative integral numbers and w is unity, or some one of 
the singular units composed with a. 

The principles on which the demonstration of this theorem depends are very briefly indi- 
cated in the notes presented by Dirichlet to the Berlin Academy in 1841, 1842, and 1846. 

+ Crelle’s Journal, vol. xl. p. 312. 

{ See Kronecker, De unitatibus complexis, pars altera; and Kummer, in Liouville’s Jour- 
nal, vol. xvi. p. 383. 


Thus the equation 


ea. ee 


ON THE THEORY OF NUMBERS. 125 


what follows, that the units of which we speak have been thus reduced to a 
real form. 

For all values of d greater than 5, the nuinber of systems of fundamental 
units is infinite. For if w,, w,,...%¢,—1 still represent a system of fundamental 
units, it is evident that the system E,, E,, ... E,—1, defined by the equations 


1,1 1,2 (1, #—1) 
E, = us , vee X UT gp 
(1), (2,2) (2, w—1) 
FE, =u, us a nsie.e Boe aes Me en CA 


Ewa) ae Se tea BS). | 

is also a fundamental system, if the indices (1, 1), &c. be integral numbers, 
and if the determinant 2+(1, 1)(2,2)....(—1, p—1) be equal to unity. 
And conversely, every system of fundamental units will be represented by 
the equations (A.), if in them we assign to the indices (1, 1), (2, 2), &e. 
all systems of integral values in succession consistent with the condition 
Z+(1,1)(2,2)(3, 3).--(u—I, p—1)=+£1; so that a single system of fun- 
damental units represents to us all possible systems. 

We shall also have occasion to allude to independent systems of units. A 
system of p—1 units, w,, w,,..U%,—1, is said to be independent when it is 
impossible to satisfy the equation 

ur ur ur at wee =1, 

whatever integral values are assigned to the indices 7,, %,, 2) +++ My—1> 
The equations (A.) will represent all possible systems of independent units, 
if we suppose that in them the indices (1,1), (2,2), (3,3)... receive all 
positive and negative integral values, subject only to the condition that the 
determinant A=3+(1, 1) (2,2).--(#—1, »—1) must not vanish. Every 
system of fundamental units is also independent; but not conversely. Every 
unit can be represented as a product of the powers of the units of an inde- 
pendent system ; but if the system be not also fundamental, the indices of the 
powers are not in general integral, but are fractions having denominators 
which divide A. Lastly, if ¢,(a), ¢,(a@),...- ¢u-1(@) be a system of inde- 
pendent units, the logarithmic determinant 


L.e¢,(@), L.¢,(a), aoe iewr Cr enc) A 
L.¢,(a@”), PC aP ay | ts sree ee Oe (ae Yop 


L. e(at~*), L. e(a”~*), Sey, Slee ema. )s 


in which y denotes a primitive root of X, is different from zero; and con- 
versely, if the determinant be different from zero, the system of units is inde- 
pendent. For all systems of fundamental units, the absolute value of the 
logarithmic determinant is the same; for any other independent system, its 
value is A times that least value. The quantities denoted by the symbols 
L.c,(a), L.e,(a), &c., are the arithmetical logarithms of the real units ¢,(«), 
&c., taken positively. 

43. Gauss’s Equations of the Periods——In Gauss’s theory of the division 
of the circle, it is shown that if X be a prime number, and if ef=A—1, the e 
periods of f roots cach, that is the quantities ,, 7,. 7, +++. 7,_,, defined by 
the equations 


126 REPORT—1860. 


0 , _2 ay 
iy ed! + av +a? E = evatoiets seal ° 
Et vet ~2e+1 (f—Ve+1 
Beutcee! . ce aatew cteebes +a! 
~e—1 ~Ze—1 3e—1 fe—1 
Ne-=a ta? +a’ + eee tar 


(y still denoting a primitive root of \), are the roots of an irreducible equa- 
tion of order e having integral coefficients, which we shall symbolize by 


F(y)=y°+ Ay '+A,y° 7+... A, ytA,=0 


(see Disq. Arith. art. 346). This equation is of the kind called Abelian; 
that is to say, each of the e periods is a rational function of any other, in 
such a manner that we may establish the equations »,=9(»,), 7,=0(n,)s 
7;=9(n,), «+++ 25=¢(ne-1); Where it is to be observed that the coefficients 
of the function ¢ are not in general integral. The determination of the 
coefficients of the equation F(y)=0 may be effected, for any given prime A, 
and any given divisor e of A—1, by methods which, however tedious, present 
no theoretical difficulty. Every rational and integral function of the periods 
can be reduced to the form a,y,+a,n,+4,n,+ --+a,_,n,_;. If we com- 
bine the equation 1+ 7,+7,+7,+..--+7e-1=0 with the e—2 equations, 
by which 75, 79, -+-+ 5 | are expressed in that linear form, we may elimi- 
nate 7,, 7) +++ %e—1, and shall thus obtain an equation of order e, satisfied by 
No te. the equation of the periods, or F(y)=0. This is the method proposed 
by Gauss (Disq. Arith. art. 346) ; M. Kummer, instead, forms the system of 
equations 


m7 == n, f+ (0,0), +(0, 1)n, +(0,2)n.+ --- +(0,e—1)ne-1, 
mm, =2,f+(1,0)n, + 1)n,+C1,2)n,+ ---+C1,e—1)ne-1, 
oN =n, f+ (2, 0)n,+(2, 1)n, +(2, 2)n.+ eee (2, e—1)me-1, 


~ . . . 7 . . . . . . . . . . . 


Ne =Ne-1f + (e—1, 0)n, +(e—1, 1)y, +(e—1,2)n,+ eee +(e— 15 e—1)ne-1, 


and eliminates 7,, 7,5 --.e—1 from them. The symbol (4, /) represents the 
number of solutions of the congruence y¥+*==1+y*+t*, mod A, w and y 
denoting any two terms of a complete system of residues for the modulus f; 
nx is zero for all values of k, excepting that 2,=1, if f be even, and m,=1, 
if f be uneven*. The systems of equations corresponding to the particular 
cases e=3, e=4, have been given by Gauss, who has succeeded in expressing 
the values of the coefficients (2, 2) in each of those cases by means of num- 
bers depending on the representation of \ by certain simple quadratic forms ; 
and has employed these expressions to demonstrate the criterion already men- 
tioned in this Report for the biquadratic character of the number2+. A 
third method has been given by M. Libri{: he establishes the formula 
ANL=M + n(1 +e.) + 0,(1 ben.) + +++ nea(1 Heres); 

in which N; represents the number of solutions of the congruence 

* Liouville’s Journal, vol. xvi. p. 404. 

+ Disq. Arith. art. 358, and Theor. Res. Big. arts. 14—22. 

+ See the memoir “‘ Sur la Théorie des Nombres,” in his ‘ Mémoires de Mathématique et 


de Physique,’ pp. 121,122. The notation of the memoir has been altered in the text. See 
also M. Lebesgue, in Liouville’s Journal, vol. ii. p. 287, and vol, iii. p. 113. 


ON THE THEORY OF NUMBERS. 127 


1+ai+apg+...+a,=0, mod A*. 


If S,, S,, S,... denote the sums of the powers of the roots of the equation 
F(y)=0, this formula may be written thus, — 


k.k—-1 : 
ANL=\* + 8, +heS,+——g— &S, + woe Ses, 
or, solving for S,, S,,..., 


#8.4:=2 Ne—AN at “ns oo ~(-)N, —(r=1)*. 
From this equation, when the values of N,, N,, &c., have been determined, 
S,, S,,... may be calculated, and thence by known methods the values of 
the coefficients of the equation F(y)=0. Lastly, M. Lebesgue has shown 
that, if we denote by o, the number of ways in which numbers divisible by 
d can be formed by adding together & terms of the series y°, y',. . -yA-2, sub- 
ject to the condition that no two powers of y be added the indices of which 
are congruous for the modulus e, the function (A—1)F(y) assumes the form 


ALY —o, y+ ony* "— «2. +(—1)° oe] —(y—S)'t- 

But the practical application of any of these methods is very laborious 
when X is a large number, chiefly on account of the determinations which 
they all require of the numbers of solutions of which certain congruences are 

pobre mie es a ons 
susceptible. For e=2 the equation is vty. o, or, putting 
r=2y+1, r°—(—1)"A=0. The cubic and biquadratic equations corre- 
sponding to the cases e=3 and e=4 are also known from Gauss’s investiga- 
tions. The results assume the simplest forms if we put r=ey+1. We then 


have 

(1) e=3, 4A=M?+27N?, M=1, mod 3; 7°—3Ar—AM=0. 

(2) e=4; A=A’°+B’*; A=I1, mod 4; e=(—1)% 

[7°+(1—2e)A]?—4A (r—A)?=0f. 

Though these determinations are not required in M. Kummer’s theory, we 
have nevertheless given them here, in order to facilitate arithmetical verifi- 
cations of his results. The forms of the period-equations for the case r=8 
and e=12 can (it may be added) be elicited from the results given by Jacobi 
in his note on the division of the circle (Crelle, vol. xxx. pp. 167, 168.). 

44. The Period-Equations considered as Congruences.—An arithmetical 
property of the equation F(y)=O0, which renders it of fundamental import- 
ance in the theory of complex numbers, is expressed in the following theorem. 

“If g be a prime number satisfying the congruence gf=1, mod \, the 
congruence F(y)=0, mod q, is completely resoluble, 7. e. it is possible to 
establish an indeterminate congruence of the form 


F(y)=(y—%) (y—u,) «+» (y—ue-1), mod g, 


* In this congruence 2}, 2»,... x; are & terms (the same or different) of a complete system 
of residues for the modulus ) ; and in counting the number of solutions, two solutions are to 
be considered as different in which the same places are not occupied by the same numbers. 
A simpler formula for S;,,, may be obtained by considering 2, 2g, ... 2, to represent terms 


of a system of residues prime to A, and denoting by ey, the number of solutions of M. Libri’s 
congruence on this hypothesis. We thus find 8z+1=Ayx— f* (Liouville, vol. iii. p. 116). 

+ Liouville, vol. iii. p. 119. ‘ 

= M. Lebesgue, Comptes Rendus, vol. li. p.9. Gauss has not exhibited this last equation 
in its explicit form. See Theor. Res. Big. 2. ¢. 


123 REPORT—1860. 


Ups Uyy ++ + Ue—1 Aenoting integral numbers, congruous or incongruous, mod q*.” 
: : : ee 
A particular case of this theorem, relating to the equation ae =0 


(which may of course be regarded as the equation of the A—1 periods, con- 
sisting each of a single root), is due to Euler, and is included in his theory 
of the Residues of Powers; for it follows from that theory (see art. 12 of this 
Report), that the binomial congruence x\—1=0 (and therefore also the 


x— 


congruence =0, mod g) is completely resoluble for every prime of 


the form mA+1. 

A remarkable relation subsists between the periods 7,, 7, «++ me—1 Of the 
equation F(y)=0, and the roots 2,, 0,, Uz +++ Ue—1 of the conyruence F(y)=0, 
mod g. This relation is expressed in the following theorem :— 

«“ Every equation which subsists between any two functions of the periods, 
will subsist as a congruence for the modulus g when we substitute for the 
periods the roots of the congruence F'(y)==0 taken in a certain order.” 

It is immaterial which root of the congruence we take to correspond to any 
given root of the equation. But when this correspondence has once been esta- 
blished in a single case, we must attend to the sequence which exists among 
the roots of the congruence corresponding to the sequence of the periods. 
When w,, u,, ... %e—1 are all incongruous, their order of sequence is deter- 
mined by the congruences 


U,= (4), U=O(uU,), «++. U=G(Me-1), mod g, 
which correspond to the equations 
=I)» m= GCM)» +++ + Mo = HCMe=1)» 


and which are always significant, although the coefficients of @ are frac- 
tional, because it may be proved that their denominators are prime to the 
modulus g. When w,, %;+++%e—1 are not all incongruous [an exceptional 
case which implies that g divides the discriminant of F(y)], a precisely simi- 
lar relation subsists, though it cannot be fixed in the same manner, and though 
the number of incongruous solutions of the congruence is not equal to the 
number of the periods. (See a paper by M. Kummer in Crelle’s Journal, 


* This theorem was first given by Schoenemann (Crelle, vol. xix. p. 306); his demonstra- 
tion, however, supposes that g =e,—a limitation to which the theorem itself is not subject. 
The following proof is, with a slight modification, that given by M. Kummer (Crelle, vol. xxx. 
p- 107, or Liouville, vol. xvi. p. 403). From the indeterminate congruence of Lagrange (see 
art. 10 of this Report) 

x(a—1) (w7—2)....(v—g+1) =a! —2, mod g, 
it follows that 
(y—nx) (Y—g—1) (Y= MK—2) «+ YM IFAD SY 14)" — (Yn) 


=y! — ng! — (ym) =" —y, mod g, 
observing that ,.4=n,41naq» and that, if Ind g be divisible by e (or, which is the same 
thing, if g satisfy the congruence gf=1, mod X), np41nd g=7%- Multiplying together the 
e congruences obtained by giving to & the e values of which it is susceptible in the formula 
(y—nx) Y—2¢-1) YE 2) + (Y= Me) Sy" —y, mod g, 

we find 

F(y) F(y—1) F(y—2) «-- Fy—gt )=(y?—-)*, mod g; 
whence, by a principle to which we shall have occasion to refer subsequently (see Art. 69), it 
appears that F(y) is congruous for the modulus g to a product of the form 


(y—uy) (y=) + (Y—Ue_)- 


ee 


ON THE THEORY OF NUMBERS. 129 


vol. liii. p. 142, in which he has established this fundamental proposition on 
a satisfactory basis.) 

45. Conditions for the Divisibility of the Norm of a Complex Number by 
a Real Prime*.—Instead of the complex number 


S(a)=a,+a, a+a,a’+.... +a), a\-%, 
let us now, for a moment, consider the complex number 

W(n)=e, NAC, M1 NaH +002 +Ce—1 Ne—1y 
which, with its conjugates 

Yin) =e, me, No lg Ng oe ee +Ce—1 No» 

b(n.) =e, M+¢, 1; +¢, 14 oe Sie +¢e_1 Ny 


eerste reoeeeeesere ee eoee sess ve vese 


W(ne-1) =e, Ne—1 +, No +e, Nees Ce} Ne—2 


is a function of the periods only, and is therefore a specialized form of the 
general complex number f(a); and let ¢ still denote a real prime, satisfying 
the congruence gf=1, mod d. By means of the relation subsisting between 
the equation-roots 7, 7,, -+ e—1, and the congruence-roots %,, %,) ++ We—1y 
M. Kummer has demonstrated the two following theorems :— 

(i.) “The necessary and sufficient condition that (7) should be divisible 
by q (z.e. that the coefficients ¢,, c,,...¢e—, should be all separately divi- 
sible by q) is that the e congruences 


W(u,) =e,u, +e, u,+0,U,+ .+++ +ee—1 M1 =0, mod g, 
Yu) =e,u, +e,u,te,u,t..0.+¢c-1u%, ==0, mod q 


W(Ue-1) =6, Ue-1 +6, Uy +e, U,+ . 60. +c] Ue~2 =0, mod qd 


should be simultaneously satisfied.” 

(ii.) “The necessary and sufficient condition that the norm of (7), taken 
with respect to the periods, z.e. the number (n,) p(n,)..+- W(ne-1), should 
be divisible by g, is that one of the e congruences 


Y(u,) =0, W(w,) =0,...+++b(we-1) =0, mod q, 
should be satisfied.” 


These results may be extended to any complex number f(a), by first 
reducing it to the form 


S(a)=, (n,) +a y, (n)) +a" p, (n.)+ vee fall Wye (1). 


This is always possible; for, since the f roots which compose any one 
period, ¢. g. 4,, are the roots of an equation y(a)=0 of order f, the coeffi- 
cients of which are complex integers involving the periods only}, we may 
simply divide f(a) by x(a), and the remainder will give us the expression 
of f(a) in the required form. Further, let g now denote a prime apper- 
taining to the exponent f (not merely satisfying the congruence gf =1, mod A, 
but also satisfying no congruence of lower index and of the same form). 
The two preceding theorems are then replaced by the two following, which 
are analogous to them, and include them. 


* The outline of the theory of complex numbers contained in this and the subsequent 
articles is chiefly derived from M. Kummer’s mémoire in Liouville, vol. xvi. p. 411. 

T Disq. Arith. art. 348. 

60. K 


130 REPORT— 1860. 


(i.) “The necessary and sufficient condition that f(a) should be divisible 
by q, is that the congruences 


(ux) =0, w, (ux) =0, aint (ux~)=0, mod g, 


should be simultaneously satisfied for every value of k.” 

(ii.) “ And the condition that the norm of f(a) should be divisible by 9, 
is that the same congruences should be satisfied for some one value of k.” 

When the congruences W, (wz )=0, Ww, (wr) =0, ... - by-1(&e) =0, mod g, 
are simultaneously satisfied, f(a) is said to be congruous to zero (mod q), for 
the substitution n,=u; These f congruences may be replaced by a single 
congruence in either of two different ways. Thus, if we denote by F(y,) the 
complex number involving the periods only which we obtain by multiplying 
together the f complex numbers 


FA FU FO Dy sss fet eel 


it may be proved that the single congruence F (w,)==0, mod q, is precisely 
equivalent to the f congruences 


W,(uz)=0, W,(uz)=0,.... bei (ux) =0. 
Or, again, if we denote by ¥(»,) a complex number congruous to zero for 
every one of the substitutions 7,=,, 7,>=U. +--+ 4)>=Ue—1, but not con- 
gruous to zero for the substitution 7,=u, (such complex numbers, involving 
the periods only, can in every case be assigned) *, it is readily seen that the 
same f congruences are comprehended in the single formula 


W (ne-x) f (a) =0, mod g. 


The utility of this latter mode of expressing the f congruences will appear in 
the sequel: the formula F(az-)=0, mod q, is of importance, because it 
supplies an immediate demonstration of the important proposition, that “if 
a product of two factors be congruous to zero for the substitution 7,=wz, 
one or other of the factors must be congruous to zero for that substitution.” 

46. Definition of Ideal Prime Factors.—To develope the consequences of 
the preceding theorems, let us consider a prime number gq appertaining to 
the exponent f; and let us first suppose that it is capable of being expressed 
as the norm (taken with respect to the periods) of a complex number (7), 
which contains the periods of f terms only; so that 


q=(n) Cm) + +++ (me-1)- 


If the substitution of uw, in W render Y(w,)=0, mod g, we may distinguish 
the e factors of g by means of the substitutions which respectively render 
them congruous to zero; so that, for example, U(x) is the factor apper- 
taining to the substitution n, =. 

We thus obtain the theorem that if f(a) be congruous to zero, mod g, for 
any substitution »,=w,, f(a) is divisible by the factor of g appertaining to 
that substitution. For if Y(,) be that factor of g, 


S(@) _ fle)Y(n Vn)» bne-1) , 
Wn) q ; 


but f(a) d(n,) W(n,) «++ (ner) is congruous to zero, mod q, for every one of — 
the substitutions y,=w,, 4,=U,, ++» 7,=Ue—-1; it is consequently divisible 
by q; i.e. f(a) is divisible by U(m,). A useful particular case of this theo- 
rem is that wz—7,=0, mod Y(n,), if Y(w,)=0, mod q. 


* Crelle, vol. lili, p. 145. The number W(7) of this memoir possesses the property in 
question. 


ON THE THEORY OF NUMBERS. 131 


Again, it may be shown that these complex factors of g are primes in the 
most proper sense of the word: 2.e., first, that they are incapable of reso- 
lution into any two complex factors, unless one of those factors be a complex 
unit; and secondly, that if any one of them divide the product of two factors, 
it necessarily divides one or other of the two factors separately. That W(n,) 
possesses the first property is evident, because its norm is a real prime, and 
that it possesses the second is a consequence of the last theorem of Art. 4.5. 
For if W(,) divide f,(a) xf,(«), either f(a) or f(a), by virtue of that theo- 
rem, is congruous to zero (mod q) for the substitution »,=«,; that is to say, 
either f(a) or f,(a) is divisible by 1(»,). 

ow, if every prime g which appertains to the exponent f were actually 
eapable of resolution into e complex factors composed of the e periods of 
Ff roots, these factors would represent to us all the true primes to be con- 
sidered in the theory of the residues of Ath powers. And for values of J infe- 
rior to 11, perhaps to 23, this is, in fact, the case. But for higher values of 
X, the real primes appertaining to the exponent f divide themselves into two 
different groups, according as they are or are not susceptible of resolution 
into e conjugate factors. Let, then, g represent any prime appertaining to the 
exponent f, whether susceptible or not of this resolution, and let f(a) still 
denote a complex number which is rendered congruous to zero by the sub- 
stitution n,=w,; f(a) is said by M. Kummer to contain the ideal factor of q 
appertaining to the substitution n,=u,. ‘This definition is admissible, because 
it is verified, as we have just seen, when ¢ is actually resoluble into e con- 
jugate factors; and its introduction is justified, as M. Kummer observes, by 
its utility. To obtain a definition of the multiplicity of an ideal factor, we 
may employ a complex number ¥(7) possessing the property indicated in 
the last article. If of the two congruences 


C¥(n)]” f(a)=0, mod q”, 


[¥(n.)]"**f(a)=0, mod g”*+}, 
the former be satisfied, and the latter not, f(a) is said to contain 7 times 
precisely the ideal factor of g which appertains to the substitution »,=w,. 

47. Elementary Theorems relating to Ideal Factors—The following pro- 
positions are partly restatements (in conformity with the definitions now 
intreduced) of results to which we have already referred, and partly simple 
corollaries from them. They will serve to show that the elementary proper- 
ties of ordinary integers may now be transferred to complex numbers. 

(1.) A complex number is divisible by g when it contains all the ideal 
factors of g. If it contain all of those factors 2 times, but not all of them 
n+1 times, it is divisible by g”, but not by g”*!. 

(2.) The norm of a complex number is divisible by g when the complex 
number contains one of the ideal factors of g. If (counting multiple factors) 
it contain, in all, of the ideal factors of g, the norm is divisible by g’/, but 
by no higher power of g (f denoting the exponent to which g appertains). 

(3.) A product of two or more factors contains the same ideal divisors as 
its factors taken together. 

(4.) The necessary and sufficient condition that one complex number 
should be divisible by another is, that the dividend should contain all the 
_ ideal factors of the divisor at least as often as the divisor. 

(5.) Two complex numbers which contain the same ideal factors are 
identical, or else differ only by a unit factor. 

(6.) Every complex number contains a finite number of ideal prime fac- 
tors. These ideal prime factors (as well as the multiplicity of each of them) 
are perfectly determinate. 

K 2 


132 REPORT—1860. 


The prime number ) is the only real prime excluded from the preceding 
considerations. Since \=(1—a)(1—a’)..-.(1—a—}), it appears that the 
norm of 1—a is a real prime, and therefore 1—a cannot be resolved into 
the product of two factors, except one of them be a unit. Again, because 
the necessary and sufficient condition for the divisibility of a complex number 
by 1—a is that the sum of the coefficients of the complex number should 
be congruous to zero for the modulus \, and because the sum of the coeffi- 
cients of a product of complex numbers is congruous, for the modulus A, to 
the product of the sums of the coefficients of the factors, it appears that if 
the norm of a complex number is divisible by A, the complex number is itself 
divisible by 1—a; and also that if the product of two complex numbers be 
divisible by 1—a, one or other of the factors separately must be divisible by 
1—a. Hence 1—a is a true complex prime, and is the only prime factor of 
A; in fact, A=(1—a)(l—a’)... (1—ad—!)=e(a)(L—a)\-}, if e(a) denote 
. the complex unit 
1—a®? 1—a’° 1—ad-} 


ta 12 l—a 


The theorems which have preceded enable us to give a definition of the 
norm of an ideal complex number. If the ideal number contain the factor 
1—a m times, and if it besides contain &, k',k',...- prime factors of the 
primes g, q', g",.... appertaining to the exponents f, f', f", -... respectively, 
we are to understand by its norm, the positive integral number 


AM GS glES qMEF" 6.05 


a definition which, by virtue of the second proposition of this article, is 
exact in the case of an actually existing number. 

It will be observed that the number of actual or ideal prime factors (com- 
pound of Xth roots of unity) into which a given real prime can be decom- 
posed, depends exclusively on the exponent to which the prime appertains 
for the modulus A. If the exponent is f, the number of ideal factors is 


aa =e. Thus, if g be a primitive root of \, g continues a prime in the 


A-1 
complex theory ; if it be a primitive root of the congruence x 7 =I, mod A, 
it is only resoluble into two conjugate prime factors. This dependence of 
the number of ideal prime factors of a given prime upon the exponent to 
which it appertains is a remarkable instance of an intimate and simple con- 
nexion between two properties of the same prime number, which appear at 
first sight to have no immediate connexion with one another. 

It may be convenient to remark that the word Ideal is sometimes used so 
as to include, and sometimes so as to exclude, actually existent complex 
numbers; but it is not apprehended that any confusion can arise from this 
ambiguity, which it is not worth while to remove at the expense of intro- 
ducing a new technical term. 


48. Classification of Ideal Numbers——An ideal number (using the term 


in its restricted sense) is incapable of being exhibited in an isolated form — 
as a complex integer; as far as has yet appeared, it has no quantitative — 


existence ; and the assertion that a given complex number contains an ideal 
factor, is only a convenient mode of expressing a certain set of congruential 
conditions which are satisfied by the coefficients of the complex number. 
Nevertheless we may, without fear of error, represent ideal numbers by the 
same symbols, f(a), F(a), ¢(a@)..., which we have employed to denote 
actually existing complex numbers, if we are only careful to remember that 
these symbols, when the numbers which they represent are ideal, admit of 


ON THE THEORY OF NUMBERS. 133 


combination by multiplication or division, but not by addition or subtraction. 
Thus f(a) x f(a), f(«)+f,(«), [f(«)]”; are significant symbols, and their 
interpretation is contained in what has preceded; but we have no general 
interpretation of a combination such as f(@)+f,(«), or S(«)—f(«)*. This 
symbolic representation of ideal numbers is very convenient, and tends to 
abbreviate many demonstrations. 


Every ideal number is a divisor of an actual number, and, indeed, of an 
infinite number of actual numbers. Also, if the ideal number ¢(a) be a 
divisor of the actual number F(a), the quotient ¢,(a)=F(a) +¢(«) is always 
ideal; for if ¢,(a) were an actual number, ¢(a), which is the quotient of 
F(a) divided by 9,(a), ought also to be an actual number, It appears, 
therefore, that there exists an infinite number of different ideal multipliers, 
which all render actual the same ideal number. It has, however, been shown 
by M. Kummer that a finite number of ideal multipliers are sufficient to 
render actual all ideal numbers whatever; so that it is possible (and that in 
an infinite number of different ways) to assign a system of ideal multipliers, 
such that every ideal number is rendered actual by one of them, and one only. 
Ideal numbers are thus distributed into a certain finite number of classes,— 
a class comprehending those numbers which are rendered actual by the same 
multiplier; and this distribution into classes is independent of the particular 
system of multipliers by which it is effected, inasmuch as it is found that if 
two ideal numbers be rendered actual by the same multiplier, every other 
multiplier which renders one of them actual will also render the other actual. 
Ideal numbers which belong to the same class are said to be egutvalent; so 
that two ideal numbers, which are each of them equivalent to a third, are 
equivalent to one another. We may regard actual numbers (which need 
no ideal multiplier) as forming the first or principal class in the distribution, 
and, consequently, as all equivalent to one another. If f(a) be equivalent to 
S(a@), and g(a) to ¢,(a), f(a) x g(a) is equivalent to f(a) x $,(a),—a result 
which is expressed by saying that “equivalent ideal numbers multiplied by 
equivalent numbers, give equivalent products;” and the class of the product 
is said to be the class compounded of the classes of the factors. 

49. Representation of Ideal Numbers as the roots of Actual Numbers.— 
An important conclusion is deducible from the theorem that the number of 
classes of ideal numbers is finite. Let f(a) be any ideal number; and let us 
consider the series of ideal numbers f(a), f(a)’, /(@)’,... These numbers 
cannot all belong to different classes; we can therefore find two different 
powers of f(a), for example [/(a)]” and [f(«)]”*”, which are equivalent 
to one another. But the equivalence of these numbers implies that [/(a@) ]” 
is equivalent to the actual number+1; ¢. e. that [/(«)]” is itself an actual 
number. We may therefore enunciate the theorem, “ Every ideal number, 
raised to a certain power, becomes an actual number.” 

The index of this power is the same for all ideal numbers of the same class, 
but may be different for different classes. By reasoning precisely similar 
to that employed by Euler in his 2nd proof of Fermat’s Theoremf, it may 
be proved that the index of the first term in the serics f(a), [/(«)]’, 
[/(@)]°..-, which is an actual number, is either equal to the whole number 
of classes, or to a submultiple of that number. This least index is said to be 
the exponent to which the class of ideal numbers containing f(a) appertains. 


* These symbols are, however, interpretable when f(a) and f,(a) belong to the same 
i ome ©) ae. is ae Xf, («) be both actual, f(«) +f, («) is the ideal quo- 
ent obtained by dividing 9 («) xf («)+¢@(«) xf, (a) by 9 (a). 

Tt See art. 10 of this Report, ‘ tye 


134 REPORT—1860. 


It would seem that for certain values of the prime A, there exist classes of 
ideal numbers appertaining to the exponent H, if H denote the number of 
classes of ideal numbers*. Such classes (when they exist) possess a property 
similar to that of the primitive roots of prime numbers ; 2. é., by compounding 
such a class continually with itself we obtain all possible classes, just as by 
continually multiplying a primitive root by itself we obtain all residues 
prime to the prime of which it is a primitive root. It has, however, been 
ascertained by M. Kummer that these primitive classes do not in all cases, 
or even in general, exist. 

The theorem of this article enables us to express ideal numbers as roots 
of actually existing complex numbers. ‘Thus, if g be a prime appertaining 
to the exponent f for the modulus X, and resoluble into the product of e con- 
jugate ideal factors ¢(n,), 9(7,), $(7,),+++$(ne_,), these ideal numbers, which 
will not in general belong to the same class, will nevertheless appertain to 
the same exponent h; so that [o(n,) 1", Co(m,)1’; ..- will all be actual num- 
bers. The power g” is therefore resoluble into the product of e actually 
existing complex factors. If we effect this resolution, and represent the 


factors of g” by &(n,), ®(n,)...., the ideal numbers $(1,); ¢(7,);++++ may be 
represented by the formule 


1 1 
(1) = [&(m,)]* o(1,) = [(,) 1" gs9)2) 

50. The Number of Classes of Ideal Numbers.—The number of classes of 
ideal numbers was first determined by Dirichlet. He effected this determi- 
nation by methods which he had previously introduced into the higher 
arithmetic, and which had already led him to a demonstration of the cele- 
brated theorem, that every arithmetical progression, the terms of which are 
prime to their common difference, contains an infinite number of prime 
numbers, and to the determination of the number of non-equivalent classes 
of quadratic forms of a given determinant t. Dirichlet’s investigation of the 
problem which we are here considering has never been published; but that 
since given by M. Kummer is probably in all essential 1espects the same, as 
it reposes on an extension of the principles developed in Dirichlet’s earlier 
memoirs. Our limits compel us to omit the details of M. Kummer’s analysis ; 
the final result, however, is, that if H denote the number of non-equivalent 


2 x a In this formula P is a quantity 


1 f i ae (7) ea 
classes of ideal numbers, H @ay=i* A 


defined by the equations 


P=9(8) 9(B°) o(8°).+.g(B*), 
0(BY=1+-y,B+ yf? + 738? + «+ +, , 


* See on this subject M. Kummer’s note “on the Irregularity of Determinants” in the 
Monatsberichte of the Berlin Academy for 1853, p. 194. M. Kummer’s investigation, 
however, is restricted to classes containing ideal numbers f(a) such that f(a)xf («*) is 
an actual number. 

+ See his memoirs on Arithmetical Progressions, in the Transactions of the Berlin Academy 
for the years 1837 (p. 45) and 1841 (p. 141), or in Liouville, vol. iv. p. 393, ix. p. 255. The 
first of these papers relates to progressions of real integers, the second to progressions of 
complex numbers of the form a+27. In the memoir “ Recherches sur diverses applications 
de V’analyse infinitésimale 4 la Théorie des Nombres” (Crelle, vol. xix. p. 24, xxi. pp. 1, 
& 134), Dirichlet has applied his method to quadratic forms having real and integral co- 
efficients; and in a subsequent memoir (Crelle, vol. xxiv. p. 291), he has extended this ap- 
plication to quadratic forms, of which the coefficients are complex numbers containing 7. 
See also Crelle, vol. xviii. p. 259, xxi. p. 98 (or the Monatsberichte for 1840, p. 49), xxii. p. 
375 (Monatsberichte for 1841, p. 190). Weshall have occasion, in a later part of this Report, 
to give an abstract of the contents of this invaluable series of memoirs. 


ae 


Be ——~ 7 eemeneii te eerie 


ed 


ON THE THEORY OF NUMBERS. 135 


B representing a primitive root of the equation B\"'=1, y a primitive root 
of the congruence y~'=1, mod X, and y,, y,) ys)++- the least positive resi- 
dues of y, y’, y*,-.. for the modulus A; A is the logarithmic determinant 
(see art. 42 of this Report) of any system of »—1 fundamental units, and 
D the logarithmic determinant of a particular system of independent but not 


fundamental units, e(a), e(a”), e av Satan an , defined by the equation 
y q 


sin ine 2ik 
BfGee)G—e) Gwe 
e(a)= (la) (Ima) + jaan hire 7. 7 = eae 
sin rae 


so that 
L.c(a),  Lee(a"), Lee(ai*), +. Lee(at +) | 
L.e(a”), L.e(a”), L.e(a), aterae Leal 
D=| 1 .e(a”), L.e(a”), L.e(a%), .... L.e(a”) 


L.e(a?” ), L.e(a), L.e(a””),...- Lee (a), 


Each of the two factors and 2 of which the value of H is com- 


Ee 
(2\)#-} ” 
posed, is separately an integral number. That z is integral isa consequence 


of the relation which exists between the logarithmic determinant of a system 
of fundamental units, and that of any system of independent units; that P is 
divisible by (20)*—* may be rendered evident from the nature of the ex- 


pression P itself*. The factor a taken by itself, represents the number of 


classes that contain ideal numbers composed with the periods of two terms 
ata, a?+a-*,.... only; or, which is the same thing, it represents the 
number of classes each of which contains the reciprocal f(a@~") of every ideal 
number f(@) comprehended in it; aye? on the other hand, is the number 
of classes of those ideal numbers which become actual by multiplication 


with their own reciprocals+. The actual calculation of the factor 2 is ex- 


tremely laborious, as it requires the preliminary investigation of a system of 
fundamental units. For the cases \=5, \=7, the trigonometrical units e(a), 
e(a"), e(a””)... ave themselves a fundamental system, so that in these two 
P 
(2A)a~ 
presents somewhat less difficulty ; and M. Kummer (though not without great 
labour) has assigned its value for all primes inferior to 100. For the 
primes 3, 5, 7, 11, 13, 17, 19, that value is unity; for 23 it is 3, and then 
increases with extraordinary rapidity; so that for 97 it already amounts to 
411322823001 =3457 x 118982593. The asymptotic law of this increase 
is expressed by the formula 


cases D=A, and Rae The computation of the first factor 


* See the investigation in the next article. 
+ See the note already cited, “‘ on the Irregularity of Determinants,” in the Monatsberichte 
for 1853, p. 195. 


136 REPORT—1860. 


Lim [ Lipis pom |= 


CN aa 
when ) increases * without limit. It will be seen that the number of classes 
of ideal numbers for A=3, A=5, A=7, is unity; 7.¢., for those values of A 
every complex prime is actual. In the absence of any determination of a 
system of fundamental units for A=11, A=13, A=17, and A=19, it is not 
possible to say whether this is or is not the case for these values also. But 


from and after the limit \=93, the value of the factor indicates 


P 
a 
that a complex number is not necessarily a complex prime because it is 
irresoluble into factors. 

51. Criterion of the Divisibility of H by }.—The number of classes of 
ideal numbers, which we have symbolized by H, is not in general divisible 


by A; but in certain cases it may happen that it is so. The quotient 2 is 


never divisible by \, except when the other factor is also divisible 


lg 
2h)e-} 
by X. And it has been found by M. Kummer that the necessary and sufficient 


condition for the divisibility of by \ is that the numerator of one of 


BR 
Gry 
the first ~—1 fractions of Bernoulli should be divisible by A. The investi- 
gation of this singular criterion depends on a transformation of the function 
¢(() which enters into the expression of P. If we represent the product 
(yB—1) ¢(B)=(rn-2—-1) + (y- B+ Cyn) P? + 000 + VY, 
Ya—2)3*—*, in which every coefficient is divisible by A, by 


ALB, +B,B-+0,8+ ...B,_ 9°], or X43) 
(bm denoting the quotient a or I as ee if I represent the greatest 


integer contained in the fraction before which it is placed), we obtain by 
multiplication the equality 


(7° +1) P=d*h (B) 4B"). (BX); 
or, since y"+1 is divisible by X, and may be supposed not divisible by \°+, 


Se= HOME) HOM), 


C denoting a coefficient prime to. The congruence =0, mod A, 


P. 
(2A )R-} 
is therefore equivalent to the congruence 


¥(B) (6°) .... (B*—*) =0, mod d, 


which may, in its turn, be replaced by the following, 


Vy) Hy’). b(y*-?) =0, mod 2. 


For, if there be an equation which, considered as a congruence for a given 
modulus A, is completely resoluble for that modulus, any symmetrical function - 
of the roots of the congruence is congruous, for the modulus X, to the cor- 
responding function of the roots of the equation. The function J(() (3°) 


* Liouville, vol. xvi. p. 473. The formula is given without demonstration. 

t For y¥+1 and (y+-A)#-F1 are both of them divisible by \; but only one of them can 
be divisible by 2, since their difference is not- divisible by 2. We can therefore, without 
changing Yo 7, +++ Y,—g) determine y in accordance with the supposition in the text. 


ON THE THEORY OF NUMBERS. 137 


pete), which is a symmetric function of f, /’, ... 2, the roots of 
the equation z*+1=0, is therefore congruous to f(y) p(y") --+- d(y*-?), 
which is the same function of y, y’, y’,-.. y*~?, the roots of the congruence 
gt+1==0, mod A. Hence the necessary and sufficient condition for the 
Meeabiity of —* 


i 
Qi by \ is that one of the » congruences included in the 


formula 
Uae) ==0, mod Ny w= 1,9, 3 ..- fh -nublemths wiis., (A) 
should be satisfied. Now y~@"-» Wy”) sbiy ee rewvar) A eaYa 0 


+... +d, 57°%—)3 01, observing that y,5 y, Y2++-Ya-2 are the numbers 


1, 2, 3,...N—1, taken in a certain order, and introducing the values of 
b,, b,, by eee 


z=r—1 
yr On-Di (yn!) = gon-1 TY” mod 2. 
z=] r 
This last expression may be further transformed as follows. If f(x) denote 
22 
any function of x, and F(a)= 2 f(x), we have the identical equation 
21 
z=vA-1 a z=y—1 r 
BT ees F (1M )=@—-1) FO) 
s=1 r z=1 Y 


y and 2 being any two numbers prime to one another. To verify 
this equation, we may construct a system of unit points in a plane; 
then the right-hand member is the sum of the values of f(a) for all unit 
points in the interior of the parallelogram (0, 0), (A; 0), (A; y), (0; y); 
while the two terms of the left-hand member represent similar sums for 
the two triangles into which the parallelogram is divided by its diagonal 


ye—hy=0. Writing then in this identity a°”~* for f(x), and employing 


=F 
the symbol F,,_, (x) to represent the sum 2 2”, or rather the function 
x=1 
My 20 a gy PMV ea 
—4+i2 ike ee aa a) by ie eae Ee eras 
oe 1.an—9.0.9. Tl. 2n—4.4 Ot 
+(—1) Be. Il.2n—1 2 


ei aie 

1T.2.11.2n—2 ” 

in which B, B,... B, are the fractions of Bernoulli, and which, when x is 
an integral number, coincides with that sum, we find 


x=)A—-—1 z=y—1 ‘ 
Bars, 2 Fea | W#l=G- ri @~))- 
x=1 X= Laster 
But F,,_; (A—1)=Fhs_i (A)—\2"-1 is evidently divisible by ; so that 
x=r—1 z=y—1 
> gn + >» anes [| = 0, mod X. 
x=] 2=1 Y 


The congruences (a) may therefore be replaced by the congruences 
«x=y-—1 

D2) \ peas [P| = (), mod A, which may be written in the simpler form 
z=] Y 


138 REPORT—1860. 


z=y—1 i 
>» Bays (-;)=o moda, 
z=] v4 


2r I (y—1)A 
uf Y 


are congruous (mod 2) to the fiactions—25 >) ett Rs taken in a cer- 
PY Y 


us 
tain order. But, by a curious property of the function F,,-»» demonstrated 
for the first time by M. Kummer, 


if we observe that (A being prime to y) the numbers J 5 I 
Y 


7B Bape (—2) (LD Ba (=D. 
r=] oF + 2nyn-1 


The condition for the divisibility of H by X is therefore that one of the p 
congruences included in the formula B, (y2”"—1) =O, mod 4, should be satis- 
fied. The last of these congruences, or B, (y?—1)=0, is never satisfied ; 
for it is easily proved that the denominator of B, contains \ as a factor, 
while y2*—1=(y"+1) (y#—1), though divisible by A, is not divisible by \?. 
And since, if n<p, y2”—1 is prime to d, that factor may be omitted in the 
remaining .—] congruences ; so that the condition at which we have arrived 
coincides with that enunciated at the commencement of this article. 

We have exhibited M. Kummer’s analysis of this problem with more ful- 
ness of detail than might seem warranted by the nature of this Report, not 
only on account of its elegance, but also because it exemplifies transforma- 
tions and processes which are of frequent occurrence in arithmetical inves- 
tigation *. 

52. “ Exceptional” Primes.—A prime number X, which, like 37, 59, and 


A—3 


67 in the first hundred, divides the numerator of one of the first frac- 


tions of Bernoulli, and which consequently divides the number of classes of 
ideal numbers composed with Ath roots of unity, is termed by M. Kummer 
an exceptional prime. Such primes have to be excluded from the enunciation 
of several important propositions ; and their theory presents difficulties which 
have not yet been overcome. Thus the following propositions are true for all 
primes other than the exceptional primes, but are not true for the exceptional 
primes. 

(1.) The exponent to which any class of ideal numbers appertains (see 
art. 49) is prime to X. 

(2.) The index of the lowest power of any unit which can be expressed 
as a product of zntegral powers of the trigonometric units is prime to. For 


that index is a divisor of " (see art. 42). 


(3.) Every complex unit which is congruous to a real integer for the 
modulus A is a perfect Ath power. (Whether X be an exceptional prime or 
not, the Ath power of any complex number is congruous, for the modulus A, 
to a real integer, viz. to the sum of the coefficients of the complex number.) 


* In Liouville, vol. i. (New Series) p. 396, M. Kronecker has given a very simple demon~ 
stration of the congruence 
2ndop (y2n—1) = (y2n—1) [1294-224 . + (N—1)2n], mod 3, 
which, combined with another easily demonstrated formula, viz., 
12n4-22n +. (A—1)2n =(—1)n—1BnX, mod 2 [n <p], 
leads immediately to the theorem of M. Kummer. 


ON THE THEORY OF NUMBERS. 139 


(4.) If f(@) denote any (actual) complex number prime to d (é. e. not 
divisible by 1—a), a complex unit e (a) can always be assigned, such that 
the product F (a)=e(a) f(a) shall satisfy the two congruences 

F («) F(#—!) = [F(1)]’, moda, 

F («) =F (1), mod (1—<)’. 
A complex number satisfying these two congruential conditions is called a 
primary complex number; the product of two primary numbers is there- 
fore itself primary. This definition, in the particular case A=3, includes 
the primary numbers of art. 37, taken either positively or negatively. 

53. Fermat's Theorem for Complex Primes.—Let (a) be an actual or 
ideal complex prime, and let N=N. ¢ (a) represent its norm. A system of 
N actual numbers can always be assigned such that every complex number 
shall be congruous to one and only to one of them for the modulus ¢ (a). 
These N numbers may be said therefore to form a complete system of 
residues for the modulus ¢ (a); and by omitting the term divisible by 9 («), 
we obtain a system of N—1 residues prime to ¢ (a). 

Let g be a prime appertaining to the exponent f, so that N=@/, and let 
@ (a) or #, (no) be the prime factor of g which appertains to the substitution 
no=U ; the formula 

ata,a+a,a°+...+ar14f-], (A) 
will represent a complete system of residues for the modulus ¢, (7), if we 
assign to the coefficients dp, @,, a, .... the values 0, 1,2,...qg—1, in succession, 


For if f (@)=wWo(n0) +a, (mo) +--+... a/-! be-1 (m0) be any complex num- 
ber, f(a) is congruous for the modulus 9, (0) to Wo (%,) + api (um) +.-+af—! 
1 (uo), because up—no = 0, mod , (n,); that is, f(@) is congruous to one 
of the complex numbers included in (A); nor can any two numbers ay+ 
a,a+a,07+..+4 af, af! and 6) + 6,a+6,0°+... +b: af! included 
in that formula be congruous to one another ; for the congruence (ao>—bo) + 
a (a,—b,)+a*(a,—b,) + ... + af! (ap-1—b y_1) =0, mod ¢, (no), involves, 
by M. Kummer’s theory (see art. 45), the coexistence of the f congruences 
ao—bo =0, mod g; a,—b,=0, mod g; ..-a_1—b¢_1 =0, mod gq; ¢. e. the 
identity of the complex numbers a+ aa,+a*a,+...a¢/—laz_1, and bp +ab,+ 
@ b.+..+af/—1bz_;. It is worth while to notice that, if g be a prime ap- 
pertaining to the exponent 1, for the modulus A, @. e. if g be of the linear form 
m\+1, the real numbers 0, 1, 2, 3...g—1 will represent the terms of a 
complete system of residues for the modulus g(a); but if  (@) be a factor 
of a prime appertaining to any higher exponent than unity, a complete system 
will contain complex as well as real integral residues. 

By applying the principle (see art. 10) that a system of residues prime 
to the modulus, multiplied by a residue prime to the modulus, produces 
a system of residues prime to the modulus, we obtain the theorem, which 
here replaces Fermat’s Theorem, that if ~(a) be any actual number prime 
to » («), [y (@)]N-1=1, mod g(«). If we combine with this theorem the 
principle of Lagrange (cited in art. 11) which is valid for complex no less 
than for real prime modules, we may extend, mutatis mutandis, to the general 
complex theory the elementary propositions relating to the Residues of 
Powers, Primitive Roots, and Indices, which, as we have seen, exist in the 
ease of complex primes formed with cubic or biquadratic roots of unity. In 
fact, these propositions are of a character of even greater generality, and may 
be extended, not only to complex numbers formed with roots of unity whose 
index is a composite number, but also to all complex numbers formed with 
the roots of equations having integral coefficients, as soon as the prime fac- 
tors of those complex numbers are properly defined. 


140 REPORT—1860. 


54. M. Kummer’s Law of Reciprocity —We can now enunciate M. Kum- 
mer’s law of reciprocity. It appears, from the last article, or it may be 
proved immediately by dividing the N—1 residues of ¢(a@) into \ groups 
N-1 


of terms, after the following scheme, 
(0) Fig Tay ose) Fy 
eae 
(1) AN Oy + +++ OTN, 
A 
(2) PaO Lin» oats. 8 Fag si 
net PND 
(A—1) a\—ly,, a\—}, eeee ON 
A 
and proceeding as in art. 33 of this Report, that if ~(@) be any actual com- 
N-1 


plex number prime to ¢(@), Y(a) * is congruous for the modulus ¢(@) to 
a certain power a@* of a. This power of a may be denoted by the symbol 


tees “4 so that we have the congruence [v(a)] * = [HS], =* 


J - 
mod ¢(a@). The symbol ee roaen we may term the Atic character 


of Y (a) with regard to ¢(@), is evidently of the same nature as the corre- 
sponding symbols with which we have already met in the quadratic, cubic, 
and biquadratic theories, and admits of an extension of meaning similar to 
that of which they are susceptible. Availing himself of this symbol, M. 


Kummer has expressed his law of reciprocity by the formula eis 


Y(ay 
ACOMEN 


aon ,¢(@) and {(«) denoting real or ideal primes. But, to interpret 

%) 1» 

this equation rightly, it is important to attend to the following observations. 
(1.) When  (¢) and ¢ («) are both actual numbers, the formula supposes 

that they are both primary prime numbers. The prime 1—g is therefore 

excluded. 


(2.) The definition that we have given of the symbol [$3] becomes 
N 

unmeaning when ¢(@) is ideal, because no signification can be assigned to 
an ideal number which presents itself, not as a modulus or divisor, but as a 
residue. Let, therefore, i denote the index of the lowest power of ¢ (a) 
which is an actual number; 2. e., let 2 be the exponent to which the class of 
@ (a) appertains; and let [¢ (@) ]” represent the actually existing primary 
complex number which contains the factor ¢(«) # times, but contains no 


¢ (a) 
¢ (a) 
: : ; @ (a)* ; 
tion a perfectly definite meaning. Let then kre ] =a"; we may define 
A 


other prime factor; then the symbol [ | has by the preceding defini- 
A 


h 
the value of the symbol oe) by means of the equation Bal = 
y v(a)Ja > 2 ¥(@) 


h 
o (4) =a’, which, ¢f h be prime to , always gives a determinate value 


¥(«) 


ae 


ON THE THEORY OF NUMBERS. 141 


a for [$ Ss , k being defined by the congruence AA ==h', modi. For the 


symbol [§ 3 


however to the condition that [¢(#)]” is primary. 

It will be seen, therefore, that the exceptional primes of art. 52 are ex« 
cluded from M. Kummer’s law of reciprocity, for a twofold reason :—first, 
because if \ be one of those numbers, the definition of a primary number is 
not in general applicable; and secondly, because, on the same supposition, 


] so defined, the law of reciprocity still subsists, subject 


the symbol 2) may become unmeaning. 
“ion ad j 
55. The Theorems complementary to M. Kummer’s Law of Reciprocity.— 
The prime 1—a, and its conjugate primes, as well as the complex units, 
are excluded from the law of reciprocity; but complementary theorems by 
which the Atic characters of these numbers may be determined have been 
given by M. Kummer. For a simple unit a*, we have the formula 
k jie 
On) =a* *® , With regard to A, which is the norm of 1—a, it may be 
A 


observed that if ¢ («) be a prime factor of a real prime g appertaining, for 


‘the modulus A, to any exponent f different from unity, z.e¢. if g be not of the 


linear form m\+1, the character of every real integer, and therefore of A, 


a 
with respect to ¢ (a) is+1, because, iff> 1, q = ! 5. divisible byg—1. But 


whatever be the linear form of g, the characteristic of X or x (A) (for so we 


x 
@ («) Ja 


shall for brevity term the index of « in the equation =at), is de- 
termined by the congruence 


x)= t Da, mod A, 


LS o 
D, being the value (for v=0) of the differential coefficient ee 
Moo v\h 
if @(a@) be an actually existent number, or of yee? if it be ideal. 


To obtain the characteristics of the units, M. Kummer considers the system 


of independent units 
E, (a), E, (a), eeeee Ey-1 (a), 
defined by the formula 


—2k —4k =2(u—1)k 
—] Y 


7 Y 
Ex (a)=e(a)e(a”)  e (at) ane ne (es 
in which e(a) represents tae trigonometrical unit of art. 50, and y is the 


sale primitive root of A which occurs in the expression of e(«). We have 
then, for x [E* (q”)] and x (l—a*), the formule 


n k 2k B, 2 
x CEx (2@")] = (—1)" (y*"—1) ah D,-2%, mod X, 
PRB N—I hk? 
and x(i—at)=— >, gNoT iB pf 
ht Bd-3 
—B, Du fre ee (= 1° oS Ba 


142 REPORT—1860. 


N representing the norm of ¢ (a), B,, B,...B,-1 the fractions of Bernoulli, 
and D,,, the value of the differential coefficient 

dm log ¢ (ea (or d™ log Le (e”)}" ) for v=0. 

dvu™ hdv™ 

These formule do not in general hold for the exceptional prime numbers ), 
which divide the numerator of one of the first »—1 fractions of Bernoulli. 
This is evident from the occurrence in them of the coefficients D,,, which if 
¢ (2) be ideal, and / be divisible by \, may acquire denominators divisible 
by A, thus rendering the congruences nugatory. It is sufficient to have 
determined the characteristics of the particular system of units E, (a), E, (a), 
---E,_, («), because, as that system is independent, every other unit e (a) 
is included in the formula 

e(a)=E, (a)™ E, (a)™ «6... Ey—1 (@)™«-1; 
so that x [e(a)] may be found from the congruence 

k= 


x Le («)] =s my x [Ex (a) ], mod A, 


which cannot become unmeaning, except in the case of the exceptional 
primes, because if D! be the logarithmic determinant of the system of units 
E, (@), E, (a), 1. Ei: (a),D and A retaining the meanings assigned ng them 
in art. 50, it may be shown that D is prime to X, and therefore 2 => xis 
also prime to ); 7. e.,the denominators of the fractions m,,72,,...™,—1 are prime 
to A (see art. 42). But M. Kummer has also given a formula which assigns 
directly the characteristic of any unit e (a) whatsoever. If Ax denote the 


value of the differential coefficient ance eS). for v=0, we have 
Vv 
k=p—1 
x le(a)i] =4,Sol+3 Au, Dy_ay» mod *. 
k= 


56. We have already observed (see art. 39) that it is impossible to deduce 
a proof of the highest laws of reciprocity from the formule which pre- 
sent themselves in the theory of the division of the circle. It is true (as we 
shall presently see) that the formule IV. and V. of art. 30 determine the 
decomposition of the real prime p (supposed to be of the form 4+ 1) into its 
A—1 complex prime factors ; but it will be perceived that these complex fac- 
tors occur, not isolated, but combined ina particular manner. From equation 
IV. of the article cited we infer that p= (a) w (a); let then y (a)=f (a,) 
FS (a) «+ +f (Gy) 5 %,)&,.+%, being « different roots (of which no two are re- 


i 
ciprocals) of the equation ~ 14; so that f(a,), f(a), --~f(@,) are one- 
p q 4=1 


half of the complex primes of which p is composed ; if e(a@) be any real 
unit, satisfying the equation e(a)=e (a), it is plain that e(a,)’e(a,)’... 
e(a,)” =1, or p(a)= te(a,) f(a,) Xe(a,) f(a) --. XE (a) f(a.)- The 
consideration, therefore, of the number (a) cannot supply us with any de- 
termination of the Atic character of f(@,) which will not equally apply to 
Sf (a,)xe(a,). But for all values of \ greater than 3, the number of real 
complex units is, as we have seen, infinite; and the character of any com- 
plex prime f(a) with respect to any other complex prime evidently changes 

* The formule of this article are taken from M. Kummer’s second memoir on the com- 
plementary theorems (Crelle, vol. lvi. p. 270). 


—_" = + = 


“a 


ON THE THEORY OF NUMBERS. 143 


when f(a) is multiplied by a unit of which the Atic character is not unity. 
The inapplicability of the formule of art. 30 to any general demonstration of 
the law of reciprocity is thus apparent. The only equation of reciprocity 
that has been elicited from them is the following :— 


el (22) x.. ; (22?) =(t) x(t.) x.. x5 x 


in which ¢ (@) is a complex prime factor of a prime number p of the form 
m\+1, and q,, J.,+++-Ge are the e conjugate factors of a prime number g 
appertaining to the exponent f for the modulus X. This equation, which, if 
we adopt the generalized meaning of the symbol of reciprocity, may be writ- 


ten more briefly thus, (e%) =( q ) , was first obtained by Eisenstein, 
q Ja \o(@)/r 

who inferred it from M. Kummer’s investigation of the ideal prime divisors 
of (a) (see a note addressed by Eisenstein to Jacobi, and communicated 
by Jacobi to the Berlin Academy, in the Monatsberichte for 1850, May 30, 
p- 189). In a later memoir (Crelle’s Journal, vol. xxxix. p. 351), Eisenstein 
proposes an ingenious method—reposing, however, on an undemonstrated 
principle—for the discovery of the higher laws of reciprocity ; but it would 
seem that the application of this method failed to lead him to any definite 
result ; and it is unquestionably to M. Kummer alone that we are indebted 
for the enunciation as well as for the demonstration of the theorem. 

57. M. Kummer appears to have waited until he had developed the theory 
of complex numbers with a certain approximation to completeness, before 
proceeding to apply the principles he had discovered to the purpose which 
he had in view throughout, the investigation of the law of reciprocity. He 
succeeded in discovering the law which we have enunciated, in the year 
1847, and, after verifying it by calculated tables of some extent, he commu- 
nicated it to Dirichlet and Jacobi in January 1848, and subsequently, in 
1850, to the Berlin Academy, in a note which also contained the demonstra- 
tion of the complementary theorems relating to the units, and the prime 
divisors of X. From the analogy of the cubic theorem, it was natural to 
conjecture that the law of reciprocity would assume the simple form 


(2) =) for primes p, and p, reduced, by multiplication with proper 
anf A JA 


complex units, to a form satisfying certain congruential conditions. But 
to determine properly these conditions, 2. e. to assign the true definition 
of a primary complex prime, was no doubt the principal difficulty that M. 
Kummer had to overcome in the discovery of his theorem. If \=3, the 
single congruence f («)==f(1), mod (1—a)’, sufficiently characterizes a 
primary number; and since, whatever prime be represented by X, that con- 
gruence is satisfied by one, and one only, of the numbers included in the 
formula a* f (a), it was probable that it ought to form one of the con- 
gruential conditions included in the definition of a primary complex prime. 
In determining the second condition, M. Kummer appears to have been 
guided by a method which depends on the arithmetical properties of 


the logarithmic expansion of a complex number. If we develope log £2) 
I(@)—fQ) f(a) th 
in ascending powers of ~—2_“ \-/ and represent by L\*/ the finite num- 
oe fa) feos vinnie 
ber of terms which remain in this expansion after rejecting those which are 
congruous to zero for the modulus A, we are led, after some transformations, 
to the congruence 


144 REPORT—1860. 


Ufo = D, X, (@)+D, X, (a) +... +Dy—2 X,~2 (a), mod A, 


s=A—2 
where X; (a) represents the function = —-y~* a’, and Dy, denotes, as in 
i 
__ , Glog fe) 
art. 55, the differential coefficient EeRT In this congruence the first 


coefficient alone is altered when f(«) is multiplied by a simple unit ; and only 
the even coefficients are altered when f(a) is multiplied by a real unit. Now 
D, is rendered congruous to zero by the condition f(@) =f (1), mod (1—«)’; 
and M. Kummer has shown that, by multiplying f(a) by a properly chosen 
real unit, D,, D,,...D,—3 may be similarly made to disappear, so that we 
obtain 


-u = D, X,(a)+D, X,(a@)+ ...-+Da—2 Xa_2(a), mod d, 


a congruence which is proved to involve the second congruence of condition 
satisfied by a primary number, 2. e. f(a) f(a—!) =f(1)’, mod A*. 

58. The methods to which M. Kummer at first had recourse in order to 
obtain a demonstration of his theorem, consisted in extensions of the theory 
of the division of the circle. By such extensions he demonstrated the com- 
plementary theorems, and even a particular case of the law of reciprocity 
itself—that in which the two complex primes compared are conjugate. But, 
after repeated efforts, he found himself compelled to abandon these methods, 
and to seek elsewhere for more fertile principles. ‘I turned my attention,” 
he says, ‘to Gauss’s second demonstration of the law of quadratic recipro- 
city, which depends on the theory of quadratic forms. Though the method 
of this demonstration had never been extended to any other than quadratic 
residues, yet its principles appeared to me to be characterized by such 
generality as led me to hope that they might be successfully applied to 
residues of higher powers ; and in this expectation I was not disappointed f.” 

M. Kummer’s demonstration of the law of reciprocity was communicated 
to the Academy of Berlin in the year 1858, ten years after the date of his 
first discovery of it. An outline of the demonstration is contained in the 
Monatsberichte for that year; and it is exhibited with great clearness and 
fulness of detail in a memoir published in the Berlin Transactions for 
1859, which contains what is for the present the latest result of science on 
a problem which, if we date from the first enunciation of the quadratic 
theorem by Euler, has been studied by so many eminent geometers for 
nearly a century. It would, however, be impossible, without exceeding the 
limits within which this Report is confined, to give an account of its contents, 
which should be intelligible to persons not already familiar with the subject 
to which it refers. Taken by itself the demonstration of the theorem is, indeed, 
sufficiently simple; but it is based on a long series of preliminary researches 
relating to the complex numbers that can be formed with the roots of the 
equation w\=D («), in which D (@) itself denotes a complex number com- 
posed of Ath roots of unity. To those researches, and to the demonstration 
of the law of reciprocity founded on them, we shall again very briefly refer, 
when we come to speak of the corresponding investigations in the theory of 
quadratic forms, an acquaintance with which is essential to a comprehension 
of the method adopted by M. Kummer in his memoir. We may add that 
M. Kummer has intimated that he has already obtained two other demon- 


* Crelle, vol. xliy. p. 130-140. tT See the Berlin Transactions for 1859, p 29. 


ON THE THEORY OF NUMBERS. 145 


strations of his law of reciprocity, which, though they also depend on the 
eonsideration of complex numbers containing w, yet do not require the same 
complicated preliminary considerations. 

59. Complex Numbers composed of Roots of Unity, of which the Index is 
not a Prime.—In a special memoir (see the list in art. 41, note, No. 16), 
M. Kummer has considered the theory of complex numbers composed with 
a root of the equation w"=1, in which ” denotes a composite number. The 
primitive roots of this equation are the roots of an irreducible equation of the 
form 


Fis)— isis aor sees 9 
Tl (w?—1) 0 (w?%P—1).... 


Py» Po Py» +--+ denoting the different prime divisors of x*. If W (x) be the 
number of numbers less than 2 and prime to it, F (w) is of the order p(n), 
and every complex number containing w can be reduced (and that in one way 
only) to the form f (w)=a) +4, +a, 0°+.... +4) ,0¥-1, The 
numbers conjugate to f'(w) are the J (~) numbers obtained by writing in 
succession for w the p (7) primitive roots of w*=1; and the norm of f (w 
is the real and positive integer produced by multiplying together the w (n 
conjugates: If g be a prime number not dividing z, the sum 
Bp=w* + wht + wh? + ...., 

in which the series of terms is to be continued until it begins to repeat itself, 
is termed a period. The ~ periods w,, w,,...@, remain unchanged if for w 
we write w%, wi’, etc. Hence, if g appertain to the exponent ¢ for the modu- 


lus 7 (i. e. if g satisfy the congruence g‘ = 1, mod m, but no congruence of a 
lower order and similar form), the number of different numbers conjugate to 


? 


a given complex number containing the periods only is at most a For 
brevity, a complex number containing the periods only—for example, the 
number 
Cote, BW, +0, D+ 10+. + ln Dy 
may be symbolized by f(@,), so that 
S (@)=%+e, WebC,Wapb voce Hey Dnke 
If 1,7, 7,,...are a set fhe) numbers prime to and such that the quo- 


tient of no two of them (considered as a congruential fraction+) is congruous 
for the modulus x to any power of g, the numbers conjugate to f (a) may be 


na 

* The irreducibility of the equation % = =0 when x is a prime was first established by 
et 

Gauss (Disq. Arith. art. 341). Tor other and simpler demonstrations of the same theorem, 

see the memoirs of MM. Kronecker (Crelle, xxix. p. 280, and Liouville, 2nd series, vol. i. 

p. 399), Schoenemann (Crelle, vol. xxxi. p, 323, vol. xxxii. p. 100, & vol. xl. p- 188), Eisenstein 

(Crelle, vol.xxxix. p. 166), and Serret (Liouville, vol.xv.p.296). The principles on which these 


demonstrations depend suffice to establish the irreducibility of the equation = 
gP  —] 
but they fail, as M. Kronecker has observed, to furnish the corresponding demonstration 
when 2, as in the text, is a product of powers of different primes. This demonstration was 
first given by M. Kronecker (Liouville, vol. xix. p. 177), who has been followed by M. De- 
dekind (Crelle, vol. liv. p. 27), and by M. Arndt (id. lvi. p. 178). 
+ For the definition of a congruential fraction see art. 14. 


1860. 


146 REPORT—1860. 


represented by f (a,), f (@,); f (@,.) --+.+ The periods are the roots of 
certain irreducible equations, each of which is completely resoluble when 
considered as a congruence for the modulus g; and the roots w,, w#,,+.+ of the 
congruences are connected with the roots a, @,,...of the equations, by a 
relation precisely similar to that enunciated in art. 44. ‘This relation M. 
Kummer has established by introducing certain conjugate complex numbers* 
Y (w,), ¥ (w,), ¥ (@. ),»++- involving the periods only, not themselves divi- 
sible by g, but each satisfying the x congruences included in the formula 
Y (@,) (Sir—Uj,.) =0, mod g, 
=y heh oo owe 

From these congruences it is easy to infer that, if f (@,, @2)++++@nr) =O 
be any identical relation subsisting for the periods, a similar relation 
SF (Uys Uap oo Un) =0, mod q, will subsist for the numbers %,, %,)+++Un; for 
we find 

WY (wy) f (Bry Bary ++ = V (G,) f (uy U2. ), mod g, 

i. @.f (Uy) Uy) +++) =0, mod g. Another important property of the complex 
number ¥ (@,) is that it is congruous to zero, med gq, for every one of the sub- 
stitutions 7, =U,, 7, =Ur,, DW, =Ur,, --. except the first: thus the congruences 
WY (uy,) =0, VY (u,.) =0 are satisfied, ... but not ¥ (w,)=0, modg. If, 
then, f (w) be any complex number satisfying the congruence W (a,)" f(w) 
=0, mod g”, but not the congruence V (a,)”"+! f (w)=0, mod g”*1, f (w) 
is said to contain m times precisely the ideal factor of g corresponding to 


* These complex numbers are defined as follows (see the memoir cited at the com- 
mencement of this article, sect. 3, and that in Crelle, vol. liii. p. 142) :—Let wy, be a period 
satisfying the irreducible equation ¢ (w;,.)=0, and let a,, a,,... be the incongruous roots of 
¢ (y) =0, mod g, 4,, 5,,... the remaining terms of a complete system of residues, mod g, so 
that ¢ (b,), 9 (5.),-+-- are prime tog. Since w,/ = w;,,, mod 9, and wyy=wz, We have, 
by Lagrange’s indeterminate congruence (see art. 10 of this Report) 

(@,—-4,) (7-4)... (@E—3,) (W7,—D,) .... == 0, mod g, 
or, since w,—3, divides ¢ (4,) etc., 
(51) p (Oy) +++» (yz, —a)) (WE—Ay) .-. = 0, mod G5 
i. e. (wy —4) (@,—a,)+--.==0, mod gq. We may now consider the x series of factors 
Sy iH SL CS i Ed 

corresponding to the m values of & [the numbers a,, a,,...are of course the same for two 
periods which satisfy the same irreducible equation, but not in general the same for any — 
two periods], and, retaining among these factors only those which are different, we may 
take for ¥ (w,) the complex number formed by combining as many of them as possible, in 
such a manner as to give a product which is not divisible by g, but which is rendered divi- 
sible by g by the accession of any one factor not already contained in it. It is evident that 
W (w,) cannot contain all the factors w;,—a,, @j,—4,,---+ 5 let us then denote by wa—u a 
factor which is not contained in W (w,); we thus obtain the relation 

Y (w,) (w,—u,) =0, mod g, 
or, changing the primitive root w into w”, 

WY (a,) (w,7.—Uz,) = 0, mod 7. 

The conjugates of Y (w,) are all complex numbers formed according to the same law as 
Y (w,) itself; and, besides Y (w,) and its conjugates, no other complex number can be formed 
according to that law. Also the number w, which corresponds to a given period w;, is ab- 
solutely determined as soon as we have selected the multiplier Y (w,); for if two of the 
factors w1,—d,, Wy,—4,,... were absent from ¥ (a,) we should have V (w,) (w,—a,)=0, 
¥ (w,) (w,—4,) =0, mod g; and thence (a,—a,) Y (w,) =0, mod g, contrary to the hy- 
pothesis that a, and a, are incongruous, and that V (w,) is not divisible by g. The corre- 
spondence of the numbers w,, v,,.-.+U,, With the periods w,, @5,;-.-+@p, can thus be fixed 


in ag many ways as there are numbers conjugate to YW (w,), @ ¢. in nd ) different ways. 


ON THE THEORY OF NUMBERS. 147 


the substitution a,-=w;. Since it can be shown that the numbers conjugate 
to ¥ (a,) are all different from one another, it follows from the definition, 
that the quotient —— represents the number of conjugate ideal prime fac- 
tors contained in the real prime g, appertaining to the exponent ¢. If g bea 
divisor of 2, the definition of its ideal factors requires a certain modification, 
which we cannot here particularize. (See sect. 6 of M. Kummer’s Memoir.) 
The two definitions, corresponding to the cases of g prime to , andga 
divisor of 2, enable us, when taken together, to transfer to the general case 
when z is composite, the elementary theorems already shown to exist when 
m is prime (see art. 47). We may add that it is easy to prove, in the general 
as in the special case (see art. 48), that the number of classes of ideal num- 
bers is finite. 

60. Application to the Theory of the Division of the Circle-—We cannot 
quit the subject of complex numbers without mentioning certain important 
investigations in which they have been successfully employed. The first 
relates to the problem of the division of the circle. In this problem the 


s=p—2 
resolvent function of Lagrange = 627 (see art. 30) is, as is well 
s=0 


known, of primary importance. Retaining, with a slight modification, the 
notation of art. 30, and still representing by \ a prime divisor of p—1, and 


tee 
z ==0, let us consider the function F (a, x), 


by a root of the equation 


which is a particular case of the resolvent, and let us represent the quotient 
pate) F (a! x) by ¥z (@). We thus find 

F (att, x) 

LE @ 2) =v, (a) ¥, (a)... te s(a)F(aa), - . . (A) 
and in particular, observing that F (a, x) F (a\—!, a)=p, 

Bite. esrb (a ab. (a) .0.-Yr-a(h)y fn 6 et ew (2) 

a result which is in accordance with the known theorem that [F (a, x) ]* is 
independent of 2 and is an integral function of « only. The resolution of 
the auxiliary equation of order \, the roots of which are the ) periods of 


p—1 eP—l 
=X 


roots of the equation 7 =0, depends solely on the determination 


“e— 
of the complex numbers v, («), w, (~),..-.Wa—2(@). For when these com- 
plex numbers are known, we may equate F (a, a) to any Ath root of the ex- 
pression pw, (~) UJ, (%).-. Ya_2 (a); from the value of F (a, a), thus obtained, 

those of F(a’, 2), F(a’, a)....may be inferred by means of equation (1); 
and, lastly, from the values of F (1, x), F(a, 2), ... F (a4, 2), the values of 
the periods themselves are deducible by the solution of a system of linear 
equations. To determine the numbers w, («), ,(«),... M. Kummer assigns 
the ideal prime factors of which they are composed, employing for this pur- 
pose the results cited in art. 30. The equation yz (a) i. (a—-!)=p shows 
that Y% (a) contains precisely 1 (p—1) ideal prime divisors of p, and no other 
complex prime. To distinguish the prime factors of p contained in yy (a) 
from those contained in uz (a#-!) M. Kummer avails himself of the congruence 
V. of art. 30, viz., 


Il (m+n) 


mod p. 
Tlm.fin’ P 


Vino 


et. \!= eo, and w=y”, mod p, so that wu, u°,...w\—! are the roots of 
PAs 


148 - REPORT—1860. 


_— = 0, mod p; also, to adapt the formule of art. 30 to our present pur- 
pose, let @-"' =a, m=), n=h)N'; it will result from these substitutions, that 
We (u-") =0, mod p, if & and h satisfy the inequality [A] + [4A] >A, where 
[A] and [RA] are positive numbers less than \, and congruous, mod A, to h 
and kh respectively. If we represent by f(a) the ideal prime factor of p 
which appertains to the substitution «=u, this may be expressed by saying 


that vz(«) contains the factor f(a—"), if [i 4 Hi >, the symbols Hi 


and [FZ] denoting the least positive numbers satisfying the congruences 
L 


hx =1, mod X, and Ae=h, mod X. Assigning, therefore, to the number 

every positive value less than \ compatible with this condition, we may write 
te (a)= tar f(a-"), 

+a’ being a simple unit which may be determined by the congruence 

vz (a) = —1, mod 1—a)**: it is not necessary to add a real complex unit, 

for a reason which has already appeared (see art. 56, supra). From the 

expression for ¥z («) a still simpler formula for F (a, x) may be obtained, 


viz. m=h—] [= 
Lee rae Hy. LL ira 
n= 


61. Application to the Last Theorem of Fermat.—The second investigation 
to which we shall advert relates to the celebrated proposition known as the 


«“ Last Theorem of Fermat,” viz. that the equation 2” +y” =z” is irresoluble, 
in integral numbers, for all values of x greater than 2}. As Fermat himself 


* The numbers ;(«) are primary according to M. Kummer’s definition (art. 52); for 


F (a, x) F (ak, x) 


¥, (2) = F (e+, 2) = at, the summation extending to every pair of values of 
? 


y, and y, that satisfy the congruence y”!+-y/2=1, mod p, in which y represents the same 
primitive root of p that occurs in the expression F(#, xv). Hence ~z(1)=p—2= —1, 
mod X, and yz («) vz (2!) =p=1=[¥; (1)]*, moddA. Also ¥, («)—¥;, (1) is divisible 
by (l—«)?; for ¥%(L)=2 (y, +4y,)=3 (1 +4) (p—1) (p—2), observing that y, and y, 
each receive all the values 1, 2,...y—2 in succession. We have, therefore, the con- 
gruence ¥',, (1) ==0, mod X, from which it follows (see a note on the next article) that 
VY, (~) =, (1), mod (l—«)?, or yy, («) = —1, mod (1—<)?, as in the text. 

+ Liouville, vol. xvi. p. 448. _M. Kummer has also extended his solution of this problem 
to the case in which x is any divisor of p—1. See the memoir quoted in the last article, 
sect. 11. 

t Fermat’s enunciation of this celebrated theorem is contained in the first of the MS. notes 
placed by him on the margin of his copy of Bachet’s edition of Diophantus. It would seem 
that this copy is now lost; but in the year 1670 an edition of Bachet’s Diophantus was pub- 
lished at Toulouse, by Samuel de Fermat (the son of the great geometer), in which these 
notes are preserved (Diophanti Alexandrini Arithmeticorum libri sex, et de Numeris Mult- 
angulis liber unus, cum commentariis C. G. Bacheti V. C. et observationibus D. P. de Fermat 
senatoris Tolosani. Tolos 1670), ‘The theorems contained in them are, with a few excep- 
tions, enunciated without proof; and it may be inferred from the preface of S. Fermat, that 
he found no demonstration of thera among his father’s papers. Nevertheless, in the case of 
several of these propositions, we have the assertion of Fermat himself, that he was in posses- 
sion of their demonstration; and although, when we consider the imperfect state of analysis 
in his time, it is surprising that he should have succeeded in creating methods which sub- 
sequent inathematicians have failed to rediscover, yet there is no ground for the suspicion 
that he was guilty of an untruth, or that he mistook an apparent for a real proof. In fact 
these suspicions are refuted, not only by the reputation for honour and veracity which he 
enjoyed among his contemporaries, and by the evidence of singular clearness of insight 
which his extant writings supply, but also by the facts of the case itself. It would be inex- 


ie poy 


ON THE THEORY OF NUMBERS. 149 


has left us a proof of the impossibility of this equation in the case of n=4, 
by a method which Euler has extended to the case of m=3, we may suppose, 
without loss of generality, that 2 is an uneven prime ) greater than 3, and we 


plicable, if his conclusions reposed on induction only, that he should never have adopted an 
erroneous generalization ; and yet, with the exception of the “ Last Theorem” (the demon- 
stration of which, after two centuries, is still incomplete), every proposition of Fermat’s has 
been verified by the labours of his successors. There is, indeed, one other exception to this 
statement; but it is an exception which proves the rule. In the letter to Sir Kenelm Digby 
which concludes the ‘Commercium Epistolicum, etc.’ edited by Wallis (Oxford, 1658), 


Fermat enuntiates the proposition that the numbers contained in the formula 22”41 are all 
primes, acknowledging, however, that, though convinced of its truth, he had not succeeded 
in obtaining its demonstration. This letter, which is undated, was written in 1658; but it 
appears, from a letter of Fermat's to M. de * * *, dated October 18, 1640, that even at that 
earlier date he was acquainted with the proposition, and had convinced himself of its truth 
(D. Petri de Fermat Varia Opera Mathematica, Tolose, 1679, p. 162). It was, however, 


subsequently observed by Euler that 22°-+1=4294967297 =641 x 6700417, i.e. that the 
undemonstrated proposition is untrue (Op. Arith. collecta, vol. i. p. 356). The error, if it is 
an error, is a fortunate one for Fermat; it exemplifies his candour and veracity, and it shows 
that he did not mistake inductive probability for rigorous demonstration :—‘ Mais je vous 
adyoue tout net,” are his words in the letter last referred to, ‘‘ (car par advance je vous ad- 
vertis que comme je ne suis pas capable de m’attribuer plus que je ne scay, je dis avec meme 
franchise ce que je ne say pas) que je n’ay peu encore démonstrer l’exclusion de tous divi- 
seurs en cette belle proposition que je vous avois enyoyée, et que vous m’avez confermée 
touchant les nombres 3, 5, 17, 257, 6553, &c. Car bien que je reduise l’exclusion a la 
pluspart des nombres, et que j’aye méme des raisons probables pour le reste, je n’ay peu 
encore démonstrer nécessairement la vérité de cette proposition, de laquelle pourtant je ne 
doute non plus & cette heure que je faisois auparavant. Si vous en avez la preuve assurée, 
yous m’obligerez de me la communiquer: car aprés cela rien ne m’arrestera en ces matiéres.” 

The “ Last Theorem” is enunciated by Fermat as follows :— 

“Cubum autem in duos cubos, aut quadrato-quadratum in duos quadrato-quadratos, et 
generaliter nullam in infinitum ultra quadratum potestatem in duos ejusdem nominis fas est 
dividere ; cujus rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non 
caperet.” (Fermat’s Diophantus, p. 51.) 

Fermat has also asserted that neither the sum (ébid. p. 258) nor the difference (ibid. p.338) 
of two biquadrates can be a square. Each of these propositions comprehends the theorem 
that the sum of two biqnadrates cannot be a biquadrate; and of the second, we possess 
a yery remarkable demonstration by Fermat himself (#éd. p. 338; and compare Euler, 
Elémens d’Algébre, vol. ii. sect. 13; Legendre, Théorie des Nombres, vol.ii. p.1). The 
essential part of this demonstration consists in showing that, from any supposed solution 
of the Diophantine equation 24—y4=a square, another solution may be deduced in which 
the values of the indeterminates are not equal to zero, and yet are absolutely less than in 
the proposed solution, from which it immediately follows that the Diophantine equation 
is impossible. This method has been successfully employed by Euler (/oc. cit.) to demon- 
strate several negative Diophantine propositions, and in particular the theorem that the sum 
of two cubes cannot be acube. The only arithmetical principles (not included in the first 
elements of the science) which are employed by Euler and Fermat in their applications of 
this method, relate to certain simple properties of the quadratic forms x?+y?, 2?+2y?, 
a°+3y?; and as these principles seem inadequate to overcome the difficulties presented by 
the equation z”-+7"+2"=0, when x is > 4, it is probable that Fermat’s “ demonstratio 
mirabilis sane” of the general theorem was entirely different from that which he has inci- 
dentally given of the particular case. 

The impossibility of the equation 2”+y”+2"=0 for n=5 was first demonstrated by Le- 
gendre (Mémoires de l’Académie des Sciences, 1823, vol. vi. p. 1, or Théorie des Nombres, 
vol. ii. p. 361. See also an earlier paper by Lejeune Dirichlet, Crelle, vol. iii. p. 354, with 
the addition at p. 368, and a later one by M. Lebesgue, Liouville, vol. viii. p. 49) ; for n=14, 
by Dirichlet (Crelle, vol. ix. p. 390); and for n=7, by M. Lamé (Mémoires des Savans 
Etrangers, vol. viii. p. 421, or Liouville, vol. v. p. 295. See also the Comptes Rendus, vol. ix. 


'p- 359, and a paper by M. Lebesgue, Liouville, vol. v. pp. 276 & 348). But the methods 


employed in these researches are specially adapted to the particular exponents considered, 
and do not seem likely to supply a general demonstration. The proof in Barlow’s Theory of 
Numbers, pp. 160-169, is erroneous, as it reposes (see p. 168) on an elementary proposition 
(cor. 2, p. 20) which is untrue. A memoir by M. Kummer on the equation 24+4y4=2*, 
in which complex numbers are not employed, and in which no single case of the theorem is 


150 REPORT—!1860. 


may write the equation in the symmetrical form rrity*t2*—0, The impos- 
sibility of solving this equation has been demonstrated by M. Kummer, first, 
for all values of X not included among the exceptional primes* ; and secondly, 
for all exceptional primes which satisfy the three following conditions :— 

(1.) That the first factor of H, though divisible by A, is not divisible by 
d? (see art. 50). 

(2.) That a complex modulus can be assigned, for which a certain definite 
complex unit is not congruous to a perfect Ath power. 

(3.) That B,, is not divisible by d*, B, representing that Bernoullian 
number [xk p—1] which is divisible by \+. 

Three numbers below 100, viz. 37, 59, 67, are, as we have seen, excep- 
tional primes. But it has been ascertained by M. Kummer that the three 
conditions just given are satisfied in the case of each of those numbers; so 
that the impossibility of Fermat’s equation has been demonstrated for all 
values of the exponent up to 100. Indeed, it would probably be difficult to 
find an exceptional prime not satisfying the three conditions, and conse- 
quently excluded from M. Kummer’s demonstration. 

We must confine ourselves here to an indication of the principles on which 
the demonstration rests in the case of the non-exceptional primes f. 


demonstrated (Crelle, vol. xvii. p. 203), is nevertheless of great interest for the number of 
auxiliary propositions contained init. Of the same character are the notes by MM. Lebesgue 
and Liouville, in Liouville’s Journal, vol. vy. pp. 184 & 360, and a few theorems given with- 
out demonstration by Abel, Guvres, vol. ii. p. 264. 

In the year 1847, M. Lamé presented to the Academy at Paris a memoir containing a 
general demonstration of Fermat’s Theorem, based on the properties of complex numbers 
(Comptes Rendus, vol. xxiv. p. 310; Lionville, vol. xii. pp. 137 & 172). It was, however, 
observed by M. Liouville (Comptes Rendus, vol. xxiv. p. 315), that this demonstration is 
defective, as it assumes, without proof, the proposition that a complex number can be repre- 
sented, and in one way only, as the product of powers of complex primes—a proposition 
which, as we have seen, is untrue, unless we admit ideal as well as actual complex primes. 
The discussion on M. Lamé’s memoir attracted Cauchy’s attention to Fermat’s Theorem; and 
the 24th and 25th volumes of the Comptes Rendus contain several communications from 
him on the subject of complex numbers [or polynémes radicaux, as he has preferred to term 
them]. In the earlier papers of this series, Cauchy attempts to prove a proposition which, 
as we have already observed (see art. 41), is untrue for complex numbers considered gene- 
rally, viz. that the norm of the remainder in the division of one complex number by another 
can be rendered less than the norm of the divisor (see Comptes Rendus, vol. xxiv. pp. 517, 
633 & 661). Llsewhere (iid. p. 579) he assumes the proposition as a hypothesis, and 
deduces from it conclusions which are erroneous (pp. 581, 582). But at p. 1029 he recognizes 
and demonstrates its inaccuracy. The results at which he arrives in his subsequent papers 
on the same subject are, for the most part, comprehended in M. Kummer’s general theory 
(Comptes Rendus, vol. xxv. pp. 37, 46, 93, 132, 177). In one place, however (p. 181), he 
enunciates, though without demonstrating, the following important result :— 

“Tf the equation a+ y+2=0 be resoluble, 2, y, z denoting integral numbers prime to 
A, the sum 

fake Sees e-em et +(e 
is divisible by \.” 

(Compare M. Kummer’s memoir in the Berlin Transactions for 1857, p. 64.) 

The investigation of the Last Theorem of Fermat has been twice proposed as a prize- 
question by the Academy of Paris—first at some time previous to 1823 (see Legendre’s 
memoir already cited, in vol. vi. of the Mémoires de l’Académie des Sciences, p. 2), and again 
in 1850 (Comptes Rendus, vol. xxx. p. 263): at neither time was the prize adjudged to any 
of the memoirs received. On the last occasion, after several postponements of the date 
originally fixed for the award, the prize was ultimately, in 1857 (id. vol. xliv. p. 158), con- 
ferred on M. Kummer, who had not been a competitor, for his researches on complex num- 
bers. 

* Liouville, vol. xvi. p. 488, or Crelle, vol. xl. p. 131. 

+ See the memoir No. 15 in the list of art. 41. 


‘£ When A is not an exceptional prime, the equation v\+y\+z2*=0 is irresoluble not only 


OO 


ON THE THEORY OF NUMBERS, 151 


We may suppose that \ is greater than 3, and that no two of the numbers 
2, y, z admit any common divisor. And first, let none of them be divisible 


ak— 


by 1—a, « still representing a root of the equation =0. Since for x 


we may write a’ a, we may assume that 2, y, z are of the form 

x=a+(1—«a)’ X, 

y=b+(1—«)’ Y, 

z=c+(1—«a)’Z, 
a, b, c denoting integral numbers prime to A, which evidently satisfy the con- 
gruence a+6+c=0, mod. The equation a\+y*-+2*=0 may then be 
written thus 

(way) (a+a2y) (w@ta%y)....(atary)=—2", 
No two of the factors of which the left hand member is composed can have 
any common divisor; each of them is therefore the product of a perfect Ath 
power by a unit; so that we may write, r+a°y=a?e(a)v*, e(a) denoting 
areal unit. Since wv’ is an actual number, it follows (remembering that ) is 
not an exceptional prime) that v is also actual ; hence v* is congruous, mod A, 
to a certain integral number m. Eliminating m x e(a@) between the two con- 
gruences x+a°y==ma’e(a), and +a “y=ma °e(a), mod Xd, we find 
a °(ata’y)—a°(x+a *y)=0, mod AX. For the modulus (1—«) this 
congruence is identically satisfied*. That it should be satisfied, mod (1—«)’, 
we must have the relation (@+)p==ds, mod X; whence, putting 
b 


—— =k, mod d, 
a+b 


we have p=s, mod X. Substituting this value for p, we find that the con- 
gruence 


a" (e@tacy)—ak (a+a-*y)—0 


is identically satisfied, mod (1—«)’*; but in order that it should be satisfied, 
mod (1—a)*, we have the condition 


s°b(2k—1) (R—1)—3s(k—1 .y"+ha")=0, mod A, 


where 2 and y' are the values (for~=1) of the second derived functions 
of # and y with respect to a. This conditional congruence must be satisfied 
for every value of s; either therefore k==1, mod A, or 2R=1, mod. The 
supposition A==1 is inadmissible; for it implies that a==0, mod A, contrary 
to the hypothesis. Hence we must have 2k=1, and a=, or, by parity of 
reasoning, a=b=c, mod Xr. But alsoa+b+c=0, mod A, whence we again 
infer the inadmissible conclusion a==b==c=0, mod X. 


in ordinary integral numbers, but also in any complex integers composed of Ath roots of 
unity. The demonstration does not possess the same generality when A is an exceptional 
prime satisfying the three conditions cited in the text. In this case M. Kummer has only 
shown that the equation #\+-y*+-z\=0 is irresoluble when we suppose that 2, y, z are 
ordinary integral numbers prime to X, or else complex numbers containing the binary periods 
a+a—!, one of which has a common divisor with i. 


* Since is divisible by (1—2)"—?, and since 9(«)=9 (1)-+(@-1) ¢'()+@-I2£O 
+...,it is readily seen that, if-<X—1, the conditions for the divisibility of ¢(«) by 
(1—«)” are ¢(1)=0, ¢'(1)=0,..... ¢°-)(1)==0, mod A. 


Le REPORT—1860. 


Secondly, let one of the numbers a, y, z (for example, z) be divisible by 
1—a; it will be convenient to consider the equation in the generalized form 


a +y*=E(a)(1—a)y™2%- 2.2 26 

in which a, y, and z are all prime to 1—a@, and E(a) is any unit. We may 
assume that the values of # and y are of the form 

x=a+(1—a)’X, 

y=b+(1—a)’Y, 
a and 6 being prime to X, but satisfying the relation a+5==0, mod 2. 
In the first place, m must be greater than]. For since v4 =a, and yA’ =B, 
mod (1 —a)*+1, if a*+y* be divisible by (1—a)*, a*+0' is divisible by A’, and 
therefore x+y by (l—a)‘*". Again, each of the factors x+ay, x+a7y, 
...a+a—1y is divisible once, and once only, by l—a; whence it follows 
that x+y is divisible by (1—a)”—**", and that no two of the d factors of 
a\+y* have any other common divisor than 1—a. Hence the A factors 


Rak6 s/o e+ay atar—ly 
(l—a)ma—r>+’ et ee eee 


are relatively prime, and may be represented by expressions of the form 


2 (a) $e" e (2) o> Ch eR Oe €x-1 (a) pa-1 * 


e, (a), €, (a), ... representing units, and ¢,\, ¢,°,.... Ath powers prime to 
1—a. Eliminating x and y from the three equations 


aty =e,(a)(1—a)™—**19,%, 
ata" y=e,(a)(1—2) 4, 
+ Gs y=es (a) (1—a) os’ 


we obtain a result of the form 


gr +e (a) o\=E, (a) (1—ay™™*6., . «+ (2) 
e(a@) and E,(a) denoting two units. But, as in the former case, it may 
be shown that r* and os* are congruous, mod X, to real integers, and 
(1—a)""~?*=0, mod d, because m>1. Hence (a) is also congruous to 
a real integer for the modulus X, and _is therefore a perfect Ath power by a 


property of every non-exceptional prime (see art. 52). The equation (2) 
therefore assumes the form Te 


x +yA=E, (a) 2 (1—ayer—a, 


If, therefore, the proposed equation (1) be possible, it will follow, by suc- 
cessive applications of this reduction, that the equation 


x +y\=E (a) (1—a)* <* 


is also possible. But this equation has been shown to be impossible; the 
equation (1) is therefore also impossible. 

62. Application to the Theory of Numerical Equations.—In the Monats- 
berichte for June 20, 1853 (see also the Monatsberichte for 1856, p. 203), 
M. Kronecker has enunciated the following theorem :— 

“The roots of any Abelian equation, the coefficients of which are integral 
numbers, are rational functions of roots of unity.” The demonstration of 
this theorem (Monatsberichte for 1853, p- 371-873) depends ona compa- 


heey 


ON THE THEORY OF NUMBERS, 153 


rison of a certain form, of which the resolvent function of any Abelian 
equation is susceptible, with M. Kummer’s expression for the resolvent func- 
tion in the case of the equation of the division of the circle (see art. 60). 
It thus involves considerations relating to ideal numbers. 

Two propositions of a more special character, and closely connected with 
one another, have also been given by M. Kronecker (Crelle, vol. liii. p. 173). 
Their demonstration is immediately deducible from the principles of Dirich- 
let’s theory of complex units :— 

‘<Tf unity be the analytical modulus of every root of an equation, of which 
the first coefficient is unity and all the coefficients are integral numbers, the 
roots of the equation are roots of unity.” 

“Tf all the roots of an equation (having its first coefficient unity and all 
its coefficients integral) be real and inferior in absolute magnitude to 2, so 
that they can be represented by expressions of the form 2 cos a, 2 cos f, 
2 cos y,....the arcs a, 2, y are commensurable with the complete circum- 
ference.” 

In the following proposition M. Kronecker has extended a theorem of 
M. Kummer’s (art. 42) relating to complex units composed with roots of 
unity of which the index is a prime, to complex units composed with any 
roots of unity (Crelle, vol. liii. p. 176) :— 

« Every complex unit composed with the roots of the equation w=1, can 
be rendered real by multiplication with a 4th root of unity. If 2 be even, 
a 2nth root will always suffice; and if m be a power of a prime, an nth root 
will suffice.” 

The demonstration of this proposition is also deducible from Dirichlet’s 
principles. 

63. Tables of Complex Primes——In M. Kummer’s earliest memoir on 
complex numbers (Liouville, vol. xii. p. 206) he has given a table of the 
complex factors, composed of \th roots of unity, which are contained in real 
primes of the form m\ +1 inferior to 1000, A representing one of the primes 
5, 7,11, 13, 17, 19, 23. This memoir was written before M. Kummer had 
considered the complex factors of primes of linear forms other than mA+1, 
and before he had introduced the conception of ideal numbers. The com- 
plex prime factors of real primes of those other linear forms are, therefore, 
not exhibited in the Table; and the five numbers of the form 23m+1, 47, 
139, 277, 461, 967, each of which contains 22 ideal factors composed of 23rd 
roots of unity, are represented as products of 11 actual factors (each of 
which contains two reciprocal ideal factors). The tentative methods by 
which the complex factors were discovered are explained in sect. 9 of the 
memoir cited. Since the full development of M. Kummer’s theory, Dr. 
Reuschle has undertaken to complete and extend the Table. He has already 
given tables containing the complex prime factors of all real primes less than 
1000, composed of 5th, 7th, 11th, 13th, 17th, 23rd, and 29th roots of unity, 
together with the complete solution of the congruences corresponding to the 
equations of the periods (see the Monatsberichte for 1859, pp. 488 and 
694, and for 1860, pp. 150 and 714). For 5, 7, 11, 13, 17, the complex 
primes are exhibited in a primary form; for 19, 23, and 29 they are exhibited 
in a form which satisfies the condition f(a) = f(1), mod (I—«)?, but not 
the condition f (2) f(a-!)=[f (1)}?, mod \. The ideal factors Dr. 
Reuschle represents by their lowest actual powers; for 23 this power is the 
cube, for 29 it is the square; for 11, 13, 17, 19, as well as for 5 and 7, all 
complex prime factors of real primes less than 1000 are actual. It appears 
from the Table (and it has indeed been proved by M. Kummer), that 29 is 
an “ irregular determinant” (see art. 49, note) ; for the number of classes is 


154 REPORT—1860. 


8, while the square of every ideal number (occurring as a factor of a real 
prime inferior to 1000) is actual. The methods employed by Dr. Reuschle 
in the caiculation of his tables have not yet been published by him. In 
some instances, as M. Kummer has observed, they have not led him to the 
simplest possible forms of the ideal primes. 

A particular investigation relating to the ideal factors of 4:7, composed of 
23rd roots of unity, has been given by Mr. Cayley (Crelle, vol. lv. p. 192, 
and lvi. p. 186). 

64. The investigations relating to Laws of Reciprocity, which have so long 
occupied us in this report, have introduced us to considerations apparently 
so remote from the theory of the residues of powers of integral numbers, that 
it requires a certain effort to bear in mind their connexion with that theory. 
It will be remembered that the complex numbers to which our attention has 
been directed are not of that general kind to which we have referred in art. 41, 
but are exclusively those which are composed of roots of unity. The theory 
of complex numbers, in the widest sense of that term, does indeed present to 
us an important generalization of the theory of the residues of powers; for 
the theorem of Fermat (see art. 53) subsists alike for every species of com- 
plex numbers. But the complex numbers of Gauss, of Jacobi, and of M. 
Kummer force themselves upon our consideration, not because their proper- 
ties are generalizations of the properties of ordinary integers, but because 
certain of the properties of integral numbers can only be explained by a 
reference to them. The law of quadratic reciprocity does not, as we have 
seen, necessarily require for its demonstration any considerations other than 
those relating to ordinary integers ; the real prime numbers of arithmetic are 
here the ultimate elements that enter into the problem. But when we come 
to binomial congruences of higher orders, we find that the true elements of 
the question are no longer real primes, but certain complex factors, composed 
of roots of unity, which are, or may be conceived to be, contained in real 
primes. For we find that the law which expresses the mutual relation (with 
respect to the particular kind of congruences considered) of two of these 
complex factors is a primary and simple one; while the corresponding rela- 
tions between the real primes themselves are composite and derivative, and, in 
consequence, complicated. It thus becomes indispensable, for the investiga- 
tion of the properties of real numbers, to construct an arithmetic of complex 
integers ; and this is what has been accomplished by the researches, of which 
an account has been given in the preceding articles. 

The higher laws of reciprocity (like that of quadratic residues) may be 
considered as furnishing a criterion for the resolubility or irresolubility of 
binomial congruences ; and this, though not the only application of which they 
are susceptible, is that which most naturally suggests itself. When the bi- 
nomial congruence is cubic or biquadratic, it is easy to resolve the real prime 
modulus into factors of the form a+ dp, or a+ bi (arts. 37 and 24), and equally 
easy to determine the value of the critical symbol of reciprocity by a uni- 
form and elementary process (see art. 36). For these, therefore, as well as 
for quadratic congruences, the criterion deducible from the laws of recipro- 
city is all that can be desired. But for binomial congruences of higher 
orders this criterion is not a satisfactory one, because of the difficulty of 
obtaining the resolution of a real prime into its complex factors, and also 
because of the impossibility of determining the value of the critical symbol 
by the conversion of an ordinary fraction into a continued fraction. 

The only known criterion applicable to such congruences is the following, 
_the demonstration of which is deducible from the elements of the theory of 
the residues of powers:—Let x”==A, mod p, represent the proposed con- 


ee ee 


———-. , —_ 


— 


ON THE THEORY OF NUMBERS. 155 


gruence ; it will be resoluble or irresoluble according as the index of A is or 
is not divisible by d, the greatest common divisor of x and p—1, i.e. according 


as the exponent to which A appertains is or is not a divisor of er (see 


arts. 14 and 15). 

65. Solution of Binomial Congruences.—We now come to the problem of 
the actual solution of binomial congruences—a subject upon which our 
knowledge is confined within very narrow limits. 

When a table of indices for the prime p has been constructed, the resolu- 
tion of every binomial congruence, if it be resoluble, or, if not, the demon- 
stration of its irresolubility, is implicitly contained in it. But to use a table 
of indices for the solution of a binomial congruence is, as we have already 
observed in a similar case (art. 16), to solve a problem by means of a recorded 
solution of it. When the congruence a”==A, mod 7, is resoluble, its solu- 
tion may always be made to depend on that of a congruence of the form 
x’==a, mod p, where d is the greatest common divisor of x and p—1, and 
where aA‘, mod p, and ns==d, mod p—1. We may therefore suppose 
that, in the congruence a”==A, mod p, n is a divisor of p—1. This con- 
gruence (if resoluble at all) will have as many roots as it has dimensions; if 
— be any one of them, and 1, 0,, 6,,--.@n_, be the roots of the congruence 
x"==1, mod p, the roots of a*“==A, mod p, will be £, £0,, £0,,...£0n-1; so that 
the complete resolution of the congruence a”= A, mod p, requires, first, the 
determination of a single root of that congruence itself, and, secondly, the com- 
plete resolution of the congruence #”==1, mod p. With regard to the first of 
these requisites, in the important case in which the exponent ¢ to which A 
appertains is prime to 7, a value of x satisfying the congruence a"= A, mod p, 
can be determined by a direct method (Disq. Arith. arts. 66, 67). For, in 
this case, it will always happen that one value of z is a certain power A* of 
A, where & is determined by the congruence kn=1, mod ¢. Nor is it 
necessary, in order to determine #, to know the exponent ¢ to which A 
appertains; it is sufficient to have ascertained that it is prime to m; for, if 
we resolve p—1 into two factors prime to one another, and such that one of 
them is divisible by m and contains no prime not contained in n, the other 
will be divisible by ¢, and may be employed as modulus instead of ¢ in the 
congruence kn==1, mod¢. When this method is inapplicable, we can only 
investigate a root of the congruence #”==A, mod p-(where A is different 
from 1), by tentative processes, which, however, admit of certain abbreviations 
(Disq. Arith. arts. 67,68). The work of Poinsot (Réflexions sur la Théorie 
des Nombres, cap. iv. p. 60) contains a very full and elegant exposition of 
the theory of binomial congruences; but neither he nor any other writer 
subsequent to Gauss has been able to add any other direct method to that 
which we have just mentioned. 

66. Solution of the Congruence x"=1, mod p.—When a single root of the 
congruence x”= A is known, we may, as we have seen, complete its resolu- 
tion by obtaining all the roots of the congruence a”=1, mod p. The methods 
of Gauss, Lagrange, and Abel for the solution of the binomial equation 
x"—]=0 are in a certain sense applicable to binomial congruences of this 
special form. It is evident, from a comparison of several passages in the Dis- 
quisitiones Arithmetic *, that Gauss himself contemplated this arithmetical 
application of his theory of the division of the circle, and that he intended to 
include it in the 8th section of his work, which, however, has never been 
given to the world. In fact, the method of Abel+ which comprehends that 

* See Disq. Arith. arts. 61, 73, and especially art. 335. 

T See Abel’s memoir, “‘ Sur une classe particulicre d’équations résolubles algébriquement,”” 


156 REPORT—1860. 


of Gauss, and which gives the solution of any Abelian equation, is equally 
applicable to any Abelian congruence; zt. e. to any completely resoluble con- 
gruence of order m, the m roots of which (considered with regard to the 
prime modulus p) may be represented by the series of terms 


7, $(7)s g(r) +++. g9™—"(r), 
the symbol ¢ denoting a given rational [fractional or integral] function. 
And as we can always express the roots of an Abelian equation by radicals 
(i. e. by the roots of equations of two terms), so also the solution of an Abelian 
congruence depends ultimately on the solution of binomial congruences. 
When, for any prime modulus, an Abelian equation admits of being con- 
sidered as an Abelian congruence, so precise is the correspondence of the 
equation and the congruence, that (as Poinsot has observed in a memoir 
in which he has occupied himself with the comparative analysis of the equa- 
tion «*=1, and the congruence z”==1, mod p*) we may consider the ana- 
lytical expression of the roots of the equation as also containing an expression 
of the roots of the congruence ; and by giving a congruential interpretation T 
to the radical signs which occur in that expression, we may elicit from it the 
actual values of the roots of the congruence. An example taken from 
Poinsot’s memoir will render this intelligiblef. The six roots of the equation 


we 
= Sty are comprised in the formula 


x—1 
SLEW Eg 8 yo lh, Lid ee 
alt Nats 7 av —7 +321 Bir ii 5Vai-5V a | ; 


where the signs + and — are to be successively attributed to W —7, and 
where the product of the two cube roots is + Vor Sa according 


to the sign attributed to Va Considering the equation as a congruence 
with regard to the modulus 43, and observing that 


V —7= +6, mod 43, ¥21= +8, mod 43, 
we obtain in the first place 


‘Ov Ba yeet ey fh aad 
— atsv 16 +58 mod 43, 


Th. WA eS OL cee 

and gata s/22t gv —2 mod 43, 
the product of the two cube roots being congruous to +6 in the first formula, 
and to —6 in the second; and finally, observing that 

4/16 21, — 3, —18, mod 43, 

ee: 14, — 2, —12, mod 43, 

4/22 =—15, — 4, 19, mod 43, 

2/ —2 =+ 9, —20, +11, mod 43, 
sect. 3 (Guvres, vol.i. p. 114, or Crelle, vol. iv. p. 131), and M. Serret’s Algebre Supérieure, 
26th and 27th lessons. 

* “Sur l’Application de l’Algébre 4 la Théorie des Nombres,’’ Mémoires de l’Académie 


des Sciences, vol. iv. p. 99. 1s 
+ Gauss employs the symbol \// A, mod g, to denote a root of the congruence a" =A, mod p, 


just as he employs the symbol = mod p, to denote the root of the congruence Av=B, 


| 


ll tl il 


mod p. The congruential radical .’/ X, mod p, has of course as many values as the con- 
gruence x"= A, mod 2, has solutions; if that congruence be irresoluble, the symbol is im- 
possible. 

t See the memoir cited above, p. 125, 


bank 


ON THE THEORY OF NUMBERS. 157 


and attending to the limitation to which the cube roots are subject, 
x= —8, +11, +21, or, —2,+4, +16; mod 43. 


Thus the complete solution of a congruence of the sixth order is obtained by 
means of binomial congruences of the second and third orders only. 

An essential limitation to the usefulness of this method arises from the cir- 
cumstance that it does not always (or even in general) happen that (as in 
the example just given) each surd entering into the expression of the root 
becomes separately rational. For that expression may itself acquire a rational 
value, while certain surds contained in it continue irrational, precisely as, in 
the irreducible case of cubic equations, a real quantity is represented by an 
imaginary formula. To illustrate this point by an example, let us consider 


7 
v1 9 with respect to the modulus 29{ Here in 


the same congruence 


the expression 


—1+¥—7 1 £74 Svan | 4 5e"[ 7-3 7-3 | 
pa Sel 7g tt va +5? 7-3 —7-5v a1 |, 
where p denotes a cube root of unity, we have, putting V —7= +14, and 
p=, 


2=— + : [eva|'+5 [-5vai] » =F=1, mod 29, 
the irrational cube roots disappearing of themselves. Again, putting 
p= 3 (1+ “=3), 
we find 
w=71tiv—3(5v a )=14(5V—7)" 
=74(7)'=7416=-—6 or —9, 
where every radical becomes rational of itself. Similarly taking the values 
¥—7=—14, p=5(—1 +¥.—3), we find z=—5 or —13. But lastly, 
putting V —7=—14, p=1, we find 


r=12+ SC+7 V2)43(14—7 V2). 


To rationalize this expression, we have to observe that 147 9, relatively 
to the modulus 29, is the cube of a complex number of similar form ; in fact, 
we have (14+7V2)=(5+11¥2)*, mod 29, whence x=—4. To elicit, 
therefore, the value of this root from the irrational formula, we are obliged to 
solve the cubic congruence x°=14+7 V2, which, although of lower dimen- 
sions than the proposed congruence, is probably less easy to solve tentatively, 
because 29 has 297—1=840 residues of the form a+b¥2, and only 29—1 
=28 ordinary integral residues; so that practically the method fails. Theo- 
retically, however, the relation between the analytical expression of the 
equation-rocts and the values of the congruence-roots is of considerable 
importance, and the subject would certainly repay a closer examination 
than it has yet received. We may add that, if m be a divisor of p—1l, 
t Ibid. p. 132. 


158 REPORT— 1860. 


the complete solution of an Abelian congruence of order m requires only 
two things,—lIst, the complete solution of the congruence 2m — ] =0O, 
mod p, and, 2ndly, the determination of a single root of a certain con- 
gruence of the form #”—a==0, mod p, in which a is an ordinary integer; 


a’ —] 


so that in this case (which is that of the congruence ; =0, mod 43) 


we obtain a real, and not only an apparent reduction of the proposed con- 
gruence*. 
It should also be observed that the primitive roots of the equation 


ar—] : : ‘ achsayy 
=0 furnish, when rationalized, the primitive roots of the congruence 


a2— 
“— =0,mod p. This, the only direct method that has ever been suggested 
x 


for the determination of a primitive root, appears to be the same as that 
referred to by Gauss in the Disq. Arith. (art. 73). 

Poinsot expresses the conviction that this method of rationalization is 
applicable to any congruence corresponding to an equation, the roots of 
which can be expressed by radicals+. With regard to equations of the 
second, third, and fourth orders this is certainly true. If, for example, the 
biquadratic equation F, (z)=0O be completely resoluble when considered as 
a congruence for the modulus p, so that F, (x)= (a—a,) (w—a,) (wx—a,) 
(x—a,), mod p, it is plain that the four roots of F(#)=0, and the four 
numbers @, @,, @,, a, may be obtained by substituting, in the general formula 
which expresses the root of any biquadratic equation as an irrational function 
of its coefficients, the values of the coefficients of the functions F (a) and 
(x—a,) (w—a,) (x—a,) (w—a,) respectively. But these two sets of coeffi- 
cients differ only by multiples of p; 7. e. the values of a,, a,, a,, a, can be 
deduced from the expressions of the roots of F (v)=0 by adding multiples 
of p to the numbers which enter into those expressions. But this reasoning 
ceases to be applicable to equations of an order higher than the fourth, 
because no general formula exists representing the roots of an equation of 
the fifth or any higher order. If, therefore, F(x)=0 be an equation of the 
mth order, the roots of which can be expressed by a radical formula, and 
which is also completely resoluble when considered as a congruence for the 
modulus p, so that F(a)=(a—a,) (w—a,)...(a@—ad,), mod p, it will not 
necessarily follow that the formula which gives the roots of F(z)=0 is also 
capable (when we add multiples of p to the numbers contained in it) of 
giving the roots of (vw—a,)(xw—a,)...(a—an)=0, 7. e. the roots of the con- 
gruence F(2)==0, mod p; and thus the principle enunciated by M. Poinsot 
is, it would seem, not rigorously demonstrated. 

67. Cubie and Biquadratic Congruences.—The reduction of cubie con- 
gruences to binomial ones has been treated of by Cauchy (Exercices des 
Mathématiques, vol. iv. p. 279), and more completely by M. Oltramare 
(Crelle, vol. xlv. p. 314). Some cases of biquadratic congruences are also 
considered by Cauchy in the memoir cited, p. 286. The following criteria 
for the resolubility or irresolubility of cubic congruences include the results 
obtained by M. Oltramare, /. c., and appear sufficiently simple to deserve 
insertion here :— 

Let the given cubic congruence be 


* This will be at once evident, if we observe that when the congruence #”=1, mod p, 
is completely resoluble, its roots may be employed to replace, in Abel’s method, the roots of 
the equation 7”™—1=0. 

+ See the memoir cited above, p. 107, and M. Libri, Mémoires de Mathématique et Phy- 
sique, p. 63. 


a 


ON THE THEORY OF NUMBERS. 159 


a0?+360°+3c0+d=0, mod p, 


p denoting a prime greater than 3, which does not divide the discriminant of 
the congruence; 7. e., the number 


D= — a d+ 6abed—4ac?—4.db? +36’ e’; 

and in connexion with the congruence consider the allied system of functions * 

U=(a, b, c,d) (a, )*, 

H=(ace—0", > (ad—be), bd—c’) (2, y)’, 

®=(—a’ d+3abe— 26°, —abd+2ac?+b’ ec, acd—2b? d+ be’, 

ad*—3bed+ 2c’) (a, y)’, 
which are connected by the equation 
+ Duw’?=—4H'; 

let also w and ¢ denote the values of U and © corresponding to any given 


values of x and y, which do not render H=0, mod p. Then, if (GP )=-1 
P 
the congruence has always one and only one real root; if (=)= +1, it has 
P 


fy =e 
either three real roots, or none: viz., if a) = +1], it has three; 
3 


if (ete) p, or =p, it has none. The interpretation of the 
P 
eubic symbol of reciprocity will present no difficulty if we observe that ¥ —D, 


mod p, is a real integer if p=3n-+1, z.e. if (=)=» and that, if p=3n—1, 


el ir (> )=-1. we have V—D="—8x WID=(p—p")W ID, mod p, 


so that ¥ —D, mod p, is a complex integer involving p. It will however be 
observed that the application of the criterion requires in either case the solu- 
tion of a quadratic congruence, 7*==—D, mod p, or r°=+1D, mod p. 

Similar, but of course less simple, criteria for the resolubility or irresolu- 
bility of biquadratic congruences may be deduced from the known formule 
for the solution of biquadratic equations. 

68. Quadratie Congruences—Indirect Methods of Solution—The general 
form of a quadratic congruence is az*+2bx2+c=0, mod P;—p denoting an 
‘uneven prime modulus, and a a number prime to p. It may be immediately 
reduced to the binomial form 7*=D, mod p, by putting r=axz+6, D=0? 
—ac,mod p. ‘The number of its solutions is 2, 0, or 1, according as D is a 
quadratic residue or non-residue of p, or is divisible by p, and is therefore 


in every case expressed by the formula 1+(— ). 


If p=4n+3, and ~)=1, the congruence 7*— D==0, mod 9, is satisfied 


by 7=D"*), and r=—D”*, and is in fact resoluble by the direct method 
of art.65. But no direct method, applicable to the case when p=4n+1, 
is at present known. Two tentative methods are proposed in the sixth sec- 
tion of the Disquisitiones Arithmetic. They are both applicable to con- 
gruences with composite as well as with prime modules. This circumstance 


* See a note by Mr. Cayley in Crelle’s Journal, vol. 1. p. 285. 


yo 


160 REPORT—1860. 


is important, because, when the modulus is a very great number, we may not 
be able to tell whether it is prime or composite, and, if composite, what the 
primes are of which it is composed, although, when the prime divisors of a 
composite modulus are known, it is simplest first to solve the congruence for 
each of them separately, and afterwards (by a method to which we shall 
hereafter refer) to deduce from these solutions the solution for the given 
composite modulus. To apply the first of Gauss’s methods, the congruence 
is written in the form 77> =D-+ Py, P denoting the modulus. If in the formula 
V=D+Py we substitute for y in succession all integral values which satisfy 
the inequality —Pay<iP-Z. and select those values of V which are per- 
fect squares, their roots (taken positively and negatively) will give us all the 
solutions of the congruence. We should thus have I¢P or 1+I}P trials to 
make, I denoting the greatest integer contained in the fraction before which it 
is placed. If, however, we take any number E, greater than 2, and prime to 
P (it is simplest to take for E a prime, or power of a prime), of which the 
quadratic non-residues are @, 0, c,..., and then determine the values of a, 3, y, 
... in the congruences a==D-+aP, mod E, 5=D+£P, mod E, &c., we shall 
find that every value of y contained in one of the linear forms mE+a, 
mE+/, &c., gives rise to a value of V which is a quadratic non-residue of 
E, and which cannot, therefore, be a perfect square ; so that we may at once 
exclude these values of y from the series of numbers to be tried. A second 
excludent E! may then be taken, and by its aid another set of linear forms 
may be determined, such that no value of y contained in them can satisfy 
the congruence. Thus the number of trials may be diminished as far as 
we please. The application of this method is still further facilitated by the 
circumstance that it is not necessary actually to solve the congruences 
a=D-+aP, mod E, ... but only the single congruence D+ Py=0, mod E 
(Disq. Arith. art. 322). Gauss’s second method depends on the theory of 
quadratic forms; it supposes that the congruence is written in the form 
7?+D=0, mod P. By a tentative process (abbreviated, as in the first 
method, by the use of excludents) Gauss obtains all possible prime representa- 
tions of P by the quadratic forms of determinant —D; whence the com- 
plete solution of the congruence r+ D=0, mod P, is immediately deduced. 
This method involves the construction of a complete system of quadratic 
forms of determinant —D, or, if the prime factors of D be known, of one 
genus of forms of that system; it becomes therefore more difficult of appli- 
cation as D increases, whereas the first method is not affected by the increase 
of D. The second method, however, especially recommends itself when P is 
a very great number; in fact, if we do not employ any excludent, the number 
of trials required by the first method varies (approximately, and when P is 
a great number) as P, whereas, on the same supposition, the number of trials 
required by the second method varies as VDx VP. 

M. Desmarest (in his Théorie des Nombres) has proposed a method less 
scientific in its character than those of Gauss, but sometimes easily applicable 
in practice. He has shown that if the congruence 7+ D==0, mod P, be re- 
soluble, we can always satisfy the equation mP=2*+ Dy* with a value of 


> 
m inferior to i+; and of y not superior to 8. The demonstration of this 
theorem is not very satisfactory, and the number of trials that it still leaves 
is very great, viz. 3 Gr + s), 


The application of Gauss’s second method is rendered somewhat more uni- 


hi 


| 


| 


ed 
ys 


ON THE THEORY OF NUMBERS. 161 


form, and at the same time the necessity for constructing a system of qua- 
dratic forms of determinant —D is avoided by the following modification of 
it:—By a known property of quadratic forms, whenever the congruence 
r’ +D=0, mod P, is resoluble, the equation mP=a°+ Dy’ is resoluble for 


some value of m < 2/2. By assigning, therefore, to m all values in suc- 
cession which are inferior to that limit, and which satisfy the condition 
(5) = (5) and then obtaining (by Gauss’s method) all prime representa- 


U 
tions of the resulting products by the form x?+-Dy’, we shall have r=+ 


ff 
r=+ oie .-.. mod P, 2’, y', x", y'! etc. denoting the different pairs of values 


of x and y in the equation mP=2?+ Dy’. 

69. General Theory of Congruences.—We may infer from several passages 
in the Disquisitiones Arithmetice, that Gauss intended to give a general 
theory of congruences of every order in the 8th section of his work, and 
that, at the time of its publication, he was already in possession of the prin- 
cipal theorems relating to the subject*. These theorems were, however, 
first given by Evariste Galois, in a note published in the Bulletin de Férus- 
sac for June, 1830 (vol. xiii. p. 438), and reprinted in Liouville’s Journal, 
vol. xi. p.398. An account of Galois’s method (completed and extended in 
some respects) will be found in M. Serret’s Cours d’Algébre Supérieure, 
Jecon25. The theory has also been independently investigated by M. Schoe- 
nemann, who seems to have been unacquainted with the earlier researches of 
Galois (see Crelle’s Journal, vol. xxxi. p. 269, and vol. xxxii. p. 93). In 
several of Cauchy’s arithmetical memoirs (see in particular Exercices de 
Mathématiques, vol. i. p. 160, vol. iv. p. 217; Comptes Rendus, vol. xxiv. 
p- 1117; Exercices d’Analyse et de Physique Mathématique, vol. iv. p. 87) 
we find observations and theorems relating to it. Lastly, in a memoir in 
Crelle’s Journal (vol. liv. p. 1) M. Dedekind has given (with important 
accessions) an excellent and lucid résumé of the results obtained by his pre- 
decessors. 

In the following account of the principles of this theory, the functional 
symbols F, ¢, ,... will represent (as in general throughout this Report) 
rational and integral functions having integral coefficients; we shall use p 
to denote a prime modulus, and @ an absolutely indeterminate quantity. As 
we shall have to consider the functions F(x), f(x), (a), ete., only in relation 
to the modulus p, we shall consider two functions F, (x) and F, (2), which 
differ only by multiples of p, as identical, and we shall represent their identity 
by the congruence F, (v)=F, (x), mod p, which is equivalent to an identical 
equation of the form F,(2)=F,(«)+p)(x). The designation “modular 
function,” which has been introduced by Cauchy (Comptes Rendus, vol. xxiv. 
p- 1118) will serve (though, perhaps, not in itself very appropriate) to indicate 
that the function to which it is applied is thus considered in relation to a 


* See Disq. Arith. art. 11 and 43. 

t Galois was born October 26, 1811, and lost his life in a duel, May 30, 1832. He was 
consequently eighteen at the time of the publication of the note referred to in the text. His 
mathematical works are collected in Liouville’s Journal, vol. xi. p. 381. Obscure and frag- 
mentary as some of these papers are, they nevertheless evince an extraordinary genius, un- 
paralleled, perhaps, for its early maturity, except by that of Pascal. It is impossible to read 
without emotion the letter in which, on the day before his death and in anticipation of it, 
Galois endeavours to rescue from oblivion the unfinished researches which haye given him a 
place for ever in the history of mathematical science. 


1860. M 


162 REPORT—1860. 


prime modulus. Since in any modular function we may omit those terms 
the coefficients of which are multiples of p, we shall always suppose that 
the coefficient of the highest power of z in the function is prime to p. 

If F(w)=f, (x) xf, (w), mod p, f, (w) and f, (#) are each of them said to 
be divisors of F(x) for the modulus p, or, more briefly, modular divisors of 
F(x), or even simply divisors of F(a) when no ambiguity can arise from this 
elliptical mode of expression. If a be a function of order zero, i. e. an integral 
number prime to p, @ is a divisor, for the modulus p, of every other modular 
function; so that we may consider the p—1 terms @,, @,, @,; -.. @p—1, of a 
system of residues prime to p, as the units of this theory, and, in any set of 
p—1 associated functions 

a E(z), a, F(@)p26e. apa EC), 
we nay distinguish that one as primary in which the highest coefficient is 
congruous to unity (mod p). 

If F(#) be a function which is divisible (mod p) by no other function 
(except the units and its own associates), F(x) is said to be a prime or irre- 
ducible function for the modulus p. And it is a fundamental proposition in 
this theory, that every modular function can be expressed in one way, and 
one way only, as the product of a unit by the powers of primary irreducible 
modular functions. The demonstration of this theorem depends (precisely 
as in the case of ordinary integral numbers) on Euclid’s process for finding 
the greatest common divisor, which, it is easy to show, is applicable to the 
modular functions we are considering here. For, if o, (a) and , (a) be two 
such functions [the degree of ¢,(#) being not higher than that of @, (x)], 
we can always form the series of congruences 


$:() = (x) $.(@) +7 $4(x), mod p, 
$2(@)=9.(#) $,(@) +7, 9,(@), mod p, 


Ce et eC eC De Mie Dc Sa YS OR RSM Je Sea eer Tt CT 


in which 7,, 7, ... denote integral numbers, g,(“), g,(#),-.. modular func- 
tions, and ¢,(«), ¢,(v),-... primary modular functions, the orders of which 
are successively lower and lower, until we arrive at a congruence 


px (2) =k (2) ort (@) +7 or42(w), mod p, 


in which 7,==0, med p. The function $741 (7) is then the greatest common 
divisor (mod p) of the given functions ¢, (w) and @, (a); and, in particular, 
if 441 (@) be of order zero, those two functions are relatively prime. We 
may add that, if R be the Resultant of ¢,(#) and ¢,(«), the necessary and 
sufficient condition that these functions should have a common modular 
divisor of an order higher than zero is contained in the congruence R=0, 
mod p*—a theorem exactly corresponding to an important algebraical pro- 
position. From the nature of the process by which the greatest common 
divisor is determined, we may infer the fundamental proposition enunciated 
above, by precisely the same reasoning which establishes the corresponding 
theorem in common arithmetic. Similarly, we may obtain the solution of 
the following useful problem :—“ Given two relatively prime modular func- 
tions A,, and A,, of the orders m and m, to find two other functions, of the 
orders m—1 and m—1 respectively, which satisfy the congruence 


A ke : Gat An Rene 1 ls mod Pp 
* See Cauchy, Exercices de Mathématiques, vol. i. p. 160, or M. Libri, Mémoires de Mathé- 


matique et de Physique, pp. 73, 74. But a proof of this proposition is really contained in 
Lagrange’s Additions to Euler’s Algebra (sect. 4). 


re 


ON THE THEORY OF NUMBERS. 163 


The assertion that f(«) is a divisor of F(x), for the modulus p is for 
brevity expressed by the congruential formula 


F(«)=0, mod [p, f(#)], 


which represents an equation of the form 
F(x)=p9 (a) + f(#) 9 (2). 
Similarly the congruence F,(#)=F,(x), mod [p, f(x)], is equivalent to 


the equation 
P(e) =F) + po@) +f) Y @),- 

If f(x) be a function of order m, it is evident that any given function is 
congruous, for the compound modulus [p, f (x)] to one, and one only, of 
the p™ functions contained in the formula @,+a,¢7+ ...+@m-12™—}, in 
which a,, a,,...@m_—, may have any values from zero to p—1 inclusive. 
These p™ functions, therefore, represent a complete system of residues for 
the modulus [p, f'(2)]. 

A congruence F(X)=0, mod [p, f(z) ], is said to be solved when a func- 
tional value is assigned to X which renders the left-hand member divisible 
by f(«) for the modulus p; and the number of solutions of the congruence 
is the number of functional values (incongruous mod [p, f(#)]) which ma 
be attributed to X. The coefficients of the powers of X in the function F(X 
may be integral numbers or functions of x. The linear congruence AX=B, 
mod [p,f(«)], in which A and B denote two modular functions, is, in 
particular, always resoluble when A is prime to f(a), mod p, and admits, in 
that case, of only one solution. 

We shall now suppose that the function f(2) in the compound modulus 
Lp, f(«)] is irreducible for the modulus p,—a supposition which involves the 
consequence that, if a product of two factors be congruous to zero for the 
modulus Cp, f(«)], one, at least, of those factors is separately congruous to 
zero for the same modulus. We thus obtain the principle (cf. art. 11) that 
no congruence can have more solutions, for an irreducible compound modu- 
lus, than it has dimensions. For, if X==£, mod [p, f(x)], satisfy the con- 
gruence F,, (X)=0, mod [p, f(x)], we find 


Bn (X) == Fn (X)— Fn (2) = (X—£) Fn (X), mod [p, f(x)]; 


Fm—1 (X) denoting a new function of order m—1, whence it follows that if 
the principle be true for a congruence of m—1 dimensions, it is also true for 
one of m dimensions ; 2. e. it is true universally. 

70. Extension of Fermat's Theorem.—Let 6 denote any one of the p™—1 
residues of the modulus [p, f(x)] which are prime to f(x); it may be 
shown, by a proof exactly similar to Dirichlet’s proof of Fermat’s theorem, 


that 
Ge =1==1), mod [p, f(#)].........-.2.+- (A) 


This result, which is evidently an extension of Fermat’s theorem, involves 
several important consequences. 

It implies, in the first place, the existence of a theory of residues of powers 
of modular functions, with respect to a compound modulus, precisely similar 
to the theory of the residues of the powers of integral numbers with regard 
to a common prime modulus. A single example (taken from M. Dedekind’s 
memoir) will suffice to show the exact correspondence of the two theories. 
The modular function 6 is or is not a quadratic residue of f(«), for the 
modulus p, according as it is or is not possible to satisfy the quadratic con- 
gruence X*==0, mod [p, f(w)]. In the former case @ satisfies the congruence 

M2 


164 REPORT—1860. 


o3(p™-1) =], mod [p, f(x)]; in the latter, 04(?"-D==—1, mod [p, f()]. 
And, further, if 6, and 0, be two primary irreducible modular functions of 


the orders m and x respectively, and if we use the symbols lel and [F| to 
1 


denote the positive or negative units which satisfy the congruences 63‘?"—)) 
x= [zi]. mod (p, @,), and he hp [z| , mod (2, 0,), respectively, these 
2 


1 


two symbols are connected by the law of reciprocity [F| =(—1)”" Fe] ‘ 
2 1 


But the equation (A) admits also of an immediate application to the theory 
of ordinary congruences with a simple prime modulus. 

In that equation let us assign to @ the particular value x ; we conclude that 
the function #?”—1—1, is divisible for the modulus p by f(«), @.e. by every 
irreducible modular function of order m. Further, if d be a divisor of m, 
gP™—1—] is algebraically divisible by avP’—1 —]; whence it appears that 
gvP™—1_] is divisible, for the modulus p, by every function of which the 
order is a divisor of m. But it is easily shown that 2?”—!—1 is not divisible 
(mod p) by any other modular function, and that it cannot contain any 
multiple modular factors. Hence we have the indeterminate congruence 


vp™-1_] =I f(x), mod p, ......... sen hi 


in which f(x) denotes any primary and irreducible function, the order of 
which is a divisor of m, and the sign of multiplication [I extends to every 
value of f(x). This theorem, again, is a generalization of Lagrange’s inde- 
terminate congruence (art.10). We may infer from it that, when m is >1, 
the number of primary functions of order m, which are irreducible for the 
modulus 7, is 
m an py alee 
= [Pm 2p" + ph qa — Spi gas + ste > 

Gy» J «++ denoting the different prime divisors of m. As this expression is 
always different from zero, it follows that there exist functions of any given 
order, which are irreducible for the modulus p. 

A congruence F(a#)==0, mod p, may be considered resolved when we 
have expressed its left-hand member as a product of irreducible modular 
factors. The linear factors (if any) then give the real solutions; the factors 
of higher orders may be supposed to represent imaginary solutions. We have 
already observed that even when all the modular factors of F(«) are linear, 
we possess no general and direct method by which they can be assigned ; it 
is hardly necessary to add that the problem of the direct determination of 
modular factors of higher orders than the first, presents even greater diffi- 
culties. Nevertheless the congruence (B) enables us to advance one step 
toward the decomposition of F(2) into its irreducible factors ; for, by means 
of it, we can separate those divisors of F(«) which are of the same order, 
not, indeed, from one another, but from all its other divisors. We may first 
of all suppose that F(#) is cleared of its multiple factors, which may be 
done, as in algebra, by investigating the greatest common divisor of F() 
and I'(x) for the modulus p. The greatest common divisor (mod p) of 
F(x) and 2?-!—] will then give us the product of all the linear modular 
factors of F(x); let F(a) be divided (mod p) by that product, and let the 
quotient be F\(#); the greatest common divisor (mod py) of F,(x) and 
gP*—1—] will give us the product of the irreducible quadratic factors of F(x) ; 


ON THE THEORY OF NUMBERS. 165 


and by continuing this process, we shall obtain the partial resolution of F(x) 
to which we have referred. 

71. Imaginary Solutions of a Congruence.—We have said that the non- 
linear modular factors of F(«)==0, mod p, may be considered to represent 
imaginary solutions. These imaginary solutions can be actually exhibited, 
if we allow ourselves to assign to # certain complex values. The following 
proposition, which shows in what manner this may be effected, is due to 
Galois :-— 

“If f(#) represent an irreducible modular function of order m, the con- 


gruence 
F(6)=0, mod [p, f(x)], 


is completely resoluble when F(a) is an irreducible modular function of 
order m, or of any order the index of which is a divisor of m.” 

To establish this theorem, write 0 for 2 in equation (B); we find 62"-!—1 
==II F(@), mod p, the sign of multiplication II extending to every irreducible 
modular function having m or a divisor of m for the index of its order. 
But the congruence 6?”—!==1, mod [p, f(x)], admits of as many roots as 
it has dimensions; therefore also every divisor of 9?”—1— 1, and, in particular, 
the function F(@) considered as a congruence for the same compound modu- 
lus, admits of as many roots as it has dimensions. 

Let the order of the congruence F(0)=0, mod [p, f(«)], be 6, and let 
any one of its roots be represented by 7; it may be shown that all its roots 
are represented by the terms of the series r, 7?, 7?°,... 77°}, For, if 
F(r)=0, mod [p, f(x)], we have also F (r?)=[F(r)]?=0, mod [p,f()], 
and similarly F(7?*)==[F (r)]”°=0, mod p; so that 7, 7?, 77’, ... 7?°—} are 
all roots of F(@)==0, mod [p, f(#)]. it remains to show that these 6 func- 
tions are all incongruous, mod [p, f(x)]. If possible let rp*+*' = ppt", 
mod [p, f(x)], & and k' being less than 6; we have, raising each side of this 

6—k' b+k 6 ° ee 
congruence to the power pé—"", rP°*"==rP", mod [p, f(x) ], i.e. rP*=r, or 
rP*—1==1, mod [p, f(x)], observing that rr°=r, mod Lp, f(x) ], because 
rP’-1__] is divisible by F(r) for the modulus p- We conclude, therefore, 
that 7 is a root, mod [p, f(«)], of some irreducible modular divisor of the 
function 6?*—1—], i. e. of some irreducible function of an order lower than 6; 
because & is less than 6; r is therefore a root, mod [p, f(x) ], of two different 
irreducible modular functions, which is impossible. 

If, therefore, we suppose x to represent, not an indeterminate quantity, 
but a root of the equation f(2)=0, we may enunciate Galois’ theorem as 
follows :— 

“Every irreducible congruence of order m is completely resoluble in com- 
plex numbers composed with roots of any equation which is irreducible for 
the modulus p, and which has m or a multiple of m for the index of its order. 

“ And all its roots may be expressed as the powers of any one of them.” 

72. Congruences having Powers of Primes for their Modules.—It remains 
for us to advert to the theory of congruences wiih composite modules—a sub- 
ject to which (if we except the case of binomial congruences) it would seem 
that the attention of arithmeticians has not been much directed. We shall 
suppose, first, that the modulus is a power of a prime number. 

The theorem of Lagrange (art. 11), and the more general proposition of 
art. 69, in which it is (as we have seen) included, cannot be extended to 
congruences having powers of primes for their modules. 

Let the proposed congruence be F (a) =0, mod p™; and let us suppose 
(what is here a restriction in the generality of the problem) that the coeffi. 


166 REPORT—1860. 


cient of the highest power of x in F(x) is prime to p, or, which comes to the 
same thing, that it is unity. Let F(a#)=PXQxR...mod p,—P,Q,R, 
.-. being powers of different irreducible modular functions. 1t may then be 
shown that F (7)=P’x Q'x R’..., mod p”, where P’, Q’, R',... are fune- 
tions of the same order as P, Q, R,..., respectively congruous to them for 
the modulus p, and deducible from them by the solution of linear congru- 
ences only. We have thus the theorem that F (x), considered with respect 
to the modulus p”, can always be resolved in one way and in one way only, 
into a product of modular functions, each of which is relatively prime (for the 
modulus p) to all the rest, and is congruous (for the same modulus p) to a 
power of an irreducible function. We may therefore replace the congruence 
F (x) =0, mod p”, by the congruences P!==0, mod p”, Q’==0, mod p™, 
R'=0, mod p”,... But no general investigation appears to have been given 
of the peculiarities that may be presented by a congruence of the form 
P! =0, mod p”, in the case in which P is a power of an irreducible function 
(mod p), and not itself such a function—a supposition which implies that the 
discriminant of F (x) is divisible by p. If, however, P be itself an irreduci- 
ble function, the congruence P! =0, mod pm, gives us one and only one solu- 
tion of the given congruence if P be linear, or, if P be not linear, it may be 
considered as representing as many imaginary solutions as it has dimensions. 
In particular, if we consider the case in which all the divisors P, Q, R,... 
are linear, we obtain the theorem :— 

«« Every congruence which considered with respect to the modulus p has 
as many icongruous solutions as it has dimensions, is also completely reso- 
luble for the modulus p”, having as many roots as it has dimensions, and no 
more.” 

If «=a,, mod p, be a solution of the congruence F (x) =0, mod p, and 
if that congruence have no other root congruous to a,, the corresponding 
solution z =a m, mod p”, of the congruence F (2) ==0, mod p”, may be ob- 
tained by the solution of linear congruences only—a proposition which is in- 
cluded in a preceding and more general observation. The process is as 
follows :—If, in the equation 


F (a, +Ap)=F(a,) + Ap (a,) +2 F(a.) +00 


we determine # by the congruence oF (a,)+kF'(a,)=0, mod p, (which is 


always possible because the hypothesis that (a—a,)* is not a divisor of 
F (x), mod p, implies that F’(a,) is not divisible by p*), and then put a,== 
a,+hp, mod p’*, we have F (a,)==0, mod p*. Similarly, from the expansion 


F (a,+kp*)=F (a,) +hp? F' (a,)+..-; 


a value of & may be deduced which satisfies the congruence F (a,+kp*) =0, 
or F(a,)==0, mod p*; and so on continually until we arrive at a congruence 
of the form F(am)=0, mod p™. But when F(z) is divisible (ior the 
modulus p) by (a—a)’ or a higher power of a—a, the congruence F(«)=0, 
mod p”, is either irresoluble or has a plurality of roots incongruous for the 
modulus p”, but all congruous to a@ for tle modulus p. Thus the congruence 
(«—a)’+kp(«x—b)=0, mod p’, is irresoluble, unless a==6, mod p; whereas 
if that condition be satisfied, it admits of p incongruous solutions, comprised 
in the formula z=a+pp, mod p’, p=0, 1, 2, 3,..p—1]. 


* If F (x) =(x—a,) $ (x), mod p, where ¢ (a,) is not divisible by py, we have F’ (x) = 
» («)+(a—a,) ¢' (x), mod p, or F’ (a,) = ¢ (a), mod p. 


ON THE THEORY OF NUMBERS. 167 


73. Binomial Congruences having a Power of a Prime for their Modulus.— 
If M be any number, and Y(M) represent the number of terms in a system 
of residues prime to M, it will follow (from a principle to which we have 
already frequently referred : see arts. 10, 26, 53, 70) that every residue of that 
system satisfies the congruence a¥(™) ==], mod M,—a proposition which is 
well known as Euler’s generalization of Fermat's theorem*. In particular, 
when M=p”, we have x?”~'(p-1)==1, mod p™. This congruence has, 
consequently, precisely as many roots as it has dimensions—a property which 
is also possessed by every congruence of the form «¢=1, mod p™, d denoting 
a divisor of p"—!(p—1). This has been established by Gauss in the 3rd 
section of the Disquisitiones Arithmetice, by a particular and somewhat 
tedious method+. The simpler and more general demonstration which he 
intended to give in the 8th section}, was perhaps in principle identical with 
the following ; we exclude the case p=2, to which indeed the theorem itself 
is inapplicable :— 

Let d=dp", 6 representing a divisor of p—1, and m being < m—1; and let 
us form the indeterminate congruence 


x'—] ==(x—a,) (w—a,)....(%—az), mod p™—”, 
which is always possible, because #°—1 ==0, mod p, has 6 incongruous roots. 
It is readily seen that, if A and B represent two numbers prime to p, and if 
A==B, mod p’, A”*==B?", mod p*+s; and conversely, if A?°=B?*, mod prts, 
A=B, mod p"§. By applying this principle it may be shown that 
xp” —] = (xP"—a,P”) (xP”—a,p") .... (av"—azP"), mod p™. 
For if we divide a»"—1 by 2?"—a,”, the remainder is a,”"—1. But, 
because a,5== 1, mod p”—, a,6p” ==1, mod p”; i. e.a?”—a,P” divides v?"—] 
for the modulus p”. Similarly «2'»”—1 is divisible (mod p™) by 2"—a,P" 
ete. ; and since all these divisors are relatively prime for the modulus p, x5?" —1 
is divisible (mod p”) by their product ; 7. e., 
at" —] == (aP"—a,?”) (aP”—a,p) ... (a? —a,?”), mod p™. 

We have thus effected the resolution of «*»”—1 into factors relatively prime, 
each of which is congruous (mod p) to a power of an irreducible function ; 
since evidently (7?”—a?”") == («—a)?”", mod p. To investigate the solutions 
of x’»"— 1 ==0, mod p”, we have therefore only to consider separately the 
8 congruences included in the formula «?”==a?", mod pm. But each of 
these congruences (by virtue of the principle already referred to) admits 
precisely p” solutions, viz. the p” numbers (incongruous mod p”) which are 
congruous toa, mod p”—”. The whole number of solutions of a'»”—1 =0, 
mod p™, is therefore equal to the index dp” of the congruence. It further 
appears that the complete solution of the binomial congruence a?”—1 =0, 


may be obtained by a direct method, when the complete solution of the 
simpler congruence «'—|1==0, mod p, has been found. For we may first 


-* Euler, Comment. Arith. vol. i. p. 284. 

t Disquisitiones Arithmeticz, arts. 84—88. See also Poinsot, Reflexions sur la Théorie 
des Nombres, cap. iv. art. 6. 

} Disquisitiones Arithmeticz, art. 84. 

§ If A=B, mod pr, but not mod pr+1, we have A=B-+Apr, where & is prime to p- 
Hence A?* =(B+kp")P°=BPs>47BP%—! ptr LK ere K denoting a coefficient divisible 


by p; or AP°=B?*, mod p**”, but not mod p **”*", because £B?*—! is prime to p. This 
result implies the principle enunciated in the text. 


168 REPORT— 1860. 


(by the method given in the last article) deduce the complete solution of 
x'—1==0, mod p™~”, from that of «7—1==0, mod p; and then the roots of 
zx'p” —]==0, mod p™, can be written down at once. 

74. Primitive Roots of the Powers of a Prime.—All\ the elementary pro- 
perties of the residues of powers, considered with regard to a modulus which 
is a power of a prime number, may be deduced from the theorem just proved. 
In particular, the demonstration of the existence and number of primitive 
roots (art. 12) is applicable here also; so that we have the theorem :— 

“There are p—2 (p—1)  (p—1) residues prime to p”, the successive 
powers of any one of which represent all residues prime to p™.” These 
residues are of course the primitive roots of p”. 

If y be a primitive root of p, of the p numbers included in the formula 
y+hp (mod p’), p—1 precisely will be primitive roots of p*. For y+Ap 
is a primitive root of p* unless (y+/p)P—! =1, mod p’; and the congruence 
xzp—1==], mod p’, has always one, and only one, root congruous to y for the 
modulus p. But every primitive root of p* is a primitive root of p*, and of 
every higher power of p, as may be shown by an application of the princi- 
ple proved in a note to the last article, or, again, by observing that every 
primitive root of p”+! is necessarily congruous, for the modulus p™, to some 
primitive root of p™, and that there are p times as many primitive roots of 
p™t) as of pm. (See Jacobi’s Canon Arithmeticus, Introduction, p. xxxiii ; 
also a problem proposed by Abel in Crelle’s Journal, vol. iii. p. 12, with 
Jacobi’s answer, ibid. p. 211.) 

75. Case when the Modulus is a Power of 2.—The powers of the even 
prime 2 are excepted from the demonstrations of the two last articles—in 
fact, if m > 3,2™ has no primitive roots. Gauss, however, has shown (Disq. 
Arith. arts. 90, 91) that the successive powers of any number of the form 
8n +3 represent, for the modulus 2”, all numbers of either of the forms 82+3 
or 82+1; similarly all numbers of the forms 8%+5 and 8x+1 are repre- 
sented by successive powers of any number of the form 8z+5. If, there- 
fore, we denote by y any number of either of the two forms 82 +3 or 82+5, 
we may represent all uneven numbers less than 2” by the formula (—1)*y8, 
in which a is to receive the values O and 1, and f the values 1, 2,5,....g™-2, 
A double system of indices may thus be used to replace the simple system 
supplied by a primitive root when such roots exist. 

Tables of indices for the powers of 2, and of uneven primes inferior to 
1000, have been appended by Jacobi to his Canon Arithmeticus. 

76. Composite Modules.—-No general theory has been given of the repre- 
sentation of rational and integral functions of an indeterminate quantity as 
products of modular functions with regard to a composite modulus divisible 
by more than one prime. Aud it is possible that no advantage would be 
gained by considering the theory of congruences with composite modules 
from this general point of view. A few isolated theorems relating to par- 
ticular cases have, however, been given by Cauchy (Comptes Rendus, 
vol. xxv. p. 26, 1847). Of these the following may serve as a specimen :— 

“If the congruence I («)==0, mod M, admit as many roots as it has 
dimensions, and if, besides, the differences of these roots be all relatively 
prime to M, we have the indeterminate congruence 


F (v)=h (a—1,) (a@—r,) (w—r,) ...(e—r,,), mod M, 


k denoting the coefficient of the highest power of # in F (w).” 
But if, instead of considering the modular decomposition of the function 
F (x), we confine ourselves to the determination of the real solutions of the 


ON THE THEORY OF NUMBERS. 169 


congruence F (2) =0, mod M, it is always sufficient to consider the con- 
gruences 


F(x)=0, mod A, F(«)=0, mod B, F(x)==0, mod C, ete., .... (A) 


where AX BxC..=M, and A, B, C,.. denote powers of different primes. 
For if «=a, mod A, «= 6, mod B, X =e, mod C, denote any solutions of 
the first, second, third ... of those congruences respectively, it is evident that, 
if X be a number satisfying the congruences X =a, mod A, X =), mod B, 
X==c, mod C (and such a number can always be assigned), we shall have 
F(X) =0 for each of the modules A, B, C,.. separately, and therefore for 
the modulus M; and further, if the congruences (A) admit respectively 
a, 2, y, +. incongruous solutions, the congruence F(«)==0, mod M, will 
admit axfxXy...inall; for we can combine any solution of F(x)=0, 
mod A, with any solution of F(«)=0, mod B, and so on*. 

77. Binomial Congruences with Composite Modules —The investigation of 
the real solutions of binomial congruences depends (in the manner just stated) 
on the investigation of the real solutions of similar congruences the modules 
of which are the powers of primes. With regard to the relations by which 
these real solutions are connected with one another, little of importance has 
been added to the few observations on this subject in the Disquisitiones 
Arithmetice (art. 92). If the modulus M=p* g’ re... »P> 4 7, «+» repre- 
senting different primes, the congruence «¥(™) = 1, mod M, possesses no 
primitive roots; for if m be the least common multiple of p*—! (p—1), 
q’— (q—1), r°-! (r—1),...., 2 will be less than and a divisor of J (M). 
But evidently, if x be any residue prime to M, the congruence «»—] =O 
will be satisfied separately for the modules p+, g°, r¢,.., and therefore for the 
modulus M ; 7. e., no residue exists, the first ~(M) powers of which are incon- 
gruous, mod M. If, however, M=2p* this conclusion does not hold, since 
the least common multiple of ~ (2) and  (p”) is W (2p™) itself; and we 
find accordingly that every uneven primitive root of p™ is a primitive root of 
2p™. When, as is sometimes the case, it is convenient to employ indices to 
designate the residues prime to a given composite modulus, we must empley 
(as in the case of a power of 2) a system of multiple indices. To take the 
most general case, let M=2?° p g? r¢ ..; let wu be any number of either of the 
forms 8x+3 or 8n+5, and P, Q, R,... primitive roots of Pe Covina VEX 
spectively. Then, if x be any given number prime to M, it will always be 
possible to find a set of integral numbers en, wn», &ns Sn, Yn ++ » Satisfying the 
conditions 


(—1)*" wen==n, mod 2°; O< , <2, 0 <n < 29%, 
p*r =n, mod p*; o< an <p" (p—1), 
Qa =n, mod g?; 0<Pn <q -'(q—1), 
R”=n, mod r*; o= An < re! (r--1); 


and these numbers form a system of indices by which the residue of m for 
each of the modules 29, Ee en Noes os (and consequently for the modulus M) 


* “Tnfra [i. e, in the 8th section] congruentias quascumque secundum modulum e pluribus 
primis compositum, ad congruentias quarum modulus est primus aut primi potestas reducere 
fusius docebimus’”’ (Disq. Arith. art. 92). It is difficult to see why Gauss should haye ae 
ployed the word “ fusius” if his investigation extended no further than the elementary 
observations referred to in the text. Nevertheless it is remarkable that Gauss in the 3rd 
section of the Disq. Arith. sometimes speaks of demonstrations as obscure, which are of 
extreme simplicity when compared with one in the 4th and several in the 5th section (see in 
particular arts. 53, 55, 56). 


170 REPORT—1860. 


is completely determined. (See Dirichlet’s memoir on the Arithmetical Pro- 
gression, sect. 7, in the Berlin Memoirs for 1837.) 

78. Primitive Roots of the Powers of Complex Primes.—Dirichlet has 
shown * that, in the theory of complex numbers of the form a+ 07, the powers 
of primes of the second species (see art. 25) have primitive roots; in fact, if 
a+bi be such a prime, and N (a+i)=a*+b°=p, every primitive root of 
p™ is a primitive root of (a+4-b7)™. On the other hand, if g be a real prime 
of the form 42+3, 9” has no primitive roots in the complex theory. For in 
general, if M be any complex modulus, and M=a* lf cy ..., a, b, ce, .. being 
different complex primes, and if A=N (a), B=N (6), C=N (e), ete. the 
number of terms in a system of residues prime to M, is A*~' (A—1) B®" 
(B—-1) C’"' (C—1).... And if we denote this number by w (M), every 
residue prime to M will satisfy the congruence 

av¥(M) = 1, mod M, 


which here corresponds to Euler’s extension of Fermat's theorem. If M=g™, 


2m—2, 2 


this congruence becomes #7 (¢ —1)==1, mod g”; but it is easily shown 


that every residue prime to g™ satisfies the congruence «¥”" “—1) =], 
mod q”™; 7. e., g” has no primitive roots, because the exponent g”—! (q’—1) 
is a divisor of, and less than, g2"—-1)(q’—1). Nevertheless two numbers y 
and y', can always be assigned, of which one appertains to the exponent g™—! 
(q’—1) and the other to the exponent g”—!, and which are such that no 
power of either of them can become congruous to a power of the other, 
mod g”, without becoming congruous to unity; from which it will appear 
that every residue prime to g” may be represented by the formula y* y', if we 
give to ~ all values from 0 to (q’—1) g™—! —1 inclusive, and to y all values 
from 0 to g™—!—1 inclusive. 

The corresponding investigations for other complex numbers besides those 
of the form a+0i have not been given. 

We here conclude our account of the Theory of Congruences. The 
further continuation of this Report will be occupied with the Theories of 
Quadratic and other Homogeneous Forms. 


Additions to Part I. 


Art. 16. Legendre’s investigation of the law of reciprocity (as presented in 
the ‘ Théorie des Nombres,’ vol. i. p. 230, or in the ‘ Essai,’ ed. 2, p. 198) is 
invalid only because it assumes, without a satisfactory proof, that if a be 
a given prime of the form 42+1, a prime 0 of the form 4%+3 can always 


be assigned, satisfying the equation ; =—1]. M. Kummer (in the Memoirs 


of the Academy of Berlin for 1859, pp. 19, 20) says that this postulate is 
easily deducible from the theorem demonstrated by Dirichlet, that every 
arithmetical progression, the terms of which have no common divisor, con- 
tains prime numbers. It would follow from this, that the demonstration of 
Legendre (which depends on a very elegant criterion for the resolubility or 
irresolubility of equations of the form aa*+dy’?+cz*=0) must be regarded 
as rigorously exact (see, however, the “ Additamenta” to arts. 151, 296, 297 
of the Disq. Arith.). In the introduction to the memoir to which we have 
just referred, the reader will find some valuable observations by M. Kummer 
on the principal investigations relating to laws of reciprocity. 


* See sect. 20f the memoir, Untersuchungen iiber die Thecrie der complexen Zahlen, in 
the Berlin Memoirs for 1841. 


ON THE THEORY OF NUMBERS. 171 


Art. 20. Dirichlet’s demonstration of the formule (A) and (A’) first 
appeared in Crelle’s Journal, vol. xvii. p. 57. Some observations in this 
paper on a supposed proof of the same formule by M. Libri (Crelle, vol. ix. 
p- 187) were inserted by M. Liouville in his Journal, vol. iii. p. 3, and gave 
rise to a controversy (in the Comptes Rendus, vol. x.) between MM. Liouville 
and Libri. The concluding paragraphs of Dirichlet’s paper contain the appli- 
cation of the formule (A) and (A’) to the law of reciprocity (Gauss’s fourth 
demonstration ). 

Art. 22. From a general theorem of M. Kummer’s (see arts. 43, 44 of this 

—s 
Report), it appears that the congruence r*==(—1) * ), mod q, is or is not 
A-1 

resoluble, according as q? =+ 1, or ==—1, mod A,—a result which implies 
the theorem of quadratic reciprocity. This very simple demonstration (which 
is, however, only a transformation of Gauss’s sixth) appears first to have 
occurred to M. Liouville (see a note by M. Lebesgue in the Comptes Rendus, 
vol. li. pp. 12, 13). 


Art. 24. A note of Dirichlet’s, in Crelle, vol. lvii. p. 187, contains an ele- 
mentary demonstration of Gauss’s criterion for the biquadratic character of 
2. From the equation p=a’*+0’, we have (a+6)* =2ad, mod p, and hence 
(a+6)eP-0) == 24(P—1) at(P—)) h4(P—1) = (Qf )4(P—) at(P—), or, which is the 


same thing, 

()=en'? (2), hairs Tle Ap (A) 

But (2)=(&)=» because p==6’, mod a; and = (45 , or, ob- 
p a 


ye 
serving that 29=(a+6)’+(a—b)’, 
a+b 2 ta es) iy " 
Sal few a eee — fi(p-l) +hab 
( P )= =) ( ) 8 ja > 
since f*+1==0, mod p. Substituting these values in the equation (A), we 
find 23(p—1) = 24>, mod p, which is in fact Gauss’s criterion. 

Art. 25. In the second definition of a primary number, for “6 is uneven,” 
read “6 is even.” Although this definition has been adopted by Dirichlet in 
his memoir in Crelle’s Journal, vol. xxiv. (see p. 301), yet, in the memoir 
“Untersuchungen tiber die complexen Zahlen” (see the Berlin Memoirs for 
1841), sect. 1, he has preferred to follow Gauss. 


Art. 36. In the algorithm given in the text, the remainders p,, p,... are all 


uneven ; and the computation of the value of the symbol Po) is thus rendered 


4 
independent of the formula (iii) of art. 28. The algorithm given by Eisen- 
stein is, however, preferable, although the rule to which it leads cannot be 
expressed with the same conciseness, because the continued fraction equi- 


valent to 2° terminates more rapidly when the remainders are the least 


ia 
possible, and not necessarily uneven. 


Art. 37. In the definition of a primary number, for “@==+1,” read 
“a=—1.” But, for the purposes of the theory of cubic residues, it is 
simpler to consider the two numbers +(a+4p) as both alike primary (see 
arts. 52 and 57). 


Art. 38. Jacobi’s two theorems cannot properly be said to involve the 


172 REPORT—1860. 


cubic law of reciprocity. If (2 =1, it will follow from those theorems that 
of 3 


o a | (2) = or p*, they do not determine whether (2: =p, 
3 2 1/3 

or ps It is remarkable that these theorems, “forma genuina qua inventa 
sunt,” may be obtained by applying the criteria for the resolubility or irreso- 
lubility of cubic congruences (art.67) to the congruence r°—3Ar—\AM =0, 
mod g (art. 43), which, by virtue of M. Kummer’s theorem (art. 44), is re- 


soluble or irresoluble according as g is or is not a cubic residue of i. 


On the Performance of Steam-Vessels, the Functions of the Screw, and 
the Relations of its Diameter and Pitch to the Form of the Vessel. 
By Vice-Admiral Moorsom. 


(A communication ordered to be printed among the Reports.) 


In this the fourth paper which I now lay before the British Association, it 
may be desirable to recapitulate the points I have brought into issue, and for 
the determination of which, data, only to be obtained by experiments, are 
still wanting, viz.— 

1. There is no agreed method by which the resistance of a ship may be 
calculated under given conditions of wind and sea. 

2. The known methods are empirical, approximate only, and imply smooth 
water and no wind. 

3. The relations in which power and speed stand to form and to size are 
comparatively unknown. 

4, The relations in which the direct and resultant thrust stand to each 
other in any given screw, and how affected by the resistance of the ship, are 
undetermined. 

In order to resolve these questions, specific experiments are needed, and 
none have yet been attempted in such manner as to lead to any satisfactory 
result. 

The Steam Ship Performance Committee of the British Association have 
pressed upon successive First Lords of the Admiralty, the great value to the 
public service which must ensue if the following measures were taken, viz.— 

1. To determine, by specific experiment, the resistance, under given con- 
ditions, of certain vessels, as types; and, at the same time, to measure the 
thrust of the screw. 

2. To record the trials of the Queen’s ships, so that the performance in 
smooth water may be compared with the performance at sea, both being re- 
corded in a tabular form, comprising particulars, to indicate the characteris- 
tics of the vessel, of the engine, of the screw, and of the boiler. 

Hitherto nothing has come of these representations. 

In the paper read last year at Aberdeen, I showed, in the case of Lord 
Dufferin’s yacht ‘Erminia,’ how the absence of admitted laws of resistance 
interfered with the adjustment of her screw, and how, therefore, as a matter 
of precaution, a screw was provided capable of a thrust beyond what the 
vessel required. 

1 also showed, in the case of the Duke of Sutherland’s yacht ‘ Undine,’ how 
her screw, from being too near the surface of the water, lost a large portion 
of the ¢hrust due to its size and proportions. In other words, a screw capa- 
ble of giving out a resultant thrust in sea water of 5022 lbs., at a speed of 


ON THE PERFORMANCE OF STEAM-VESSELS. 173 


vessel of 9:26 knots an hour, did actually give out only 3805 lbs. ‘That is to 
say, the effect produced was the same as if that screw had worked in a 
fluid whose weight was about 48 Ibs. per cubic foot instead of 64 lbs. 

Tam now about to exhibit some other examples from among Her Majesty’s 
ships of war. 

The questions now before us are— 

1. The resistance of the hull below the water-line in passing through the 
water, and of the upper works, masts, rigging, &c., passing through the air, 
the weather being calm, and the water smooth. 

2. The relation in which the thrust of the screw stands to this resistance. 

[The Admiral here gave certain results from the ‘ Marlborough,’ the ‘ Re- 
nown, and the ‘Diadem,’ and proposed that a specific issue should be tried 
by means of the ‘ Diadem.’] 

What would I not give, he observed, for some well-conducted experiments 
to determine this beautiful problem of the laws which govern the action of 
the screw in sea-water! It is a problem not only interesting to science, but 
fraught with valuable results in the economical and efficient application of 
the screw propeller. 

After commenting on the performances of the U. S. corvette ‘ Niagara,’ the 
Admiral observed, I have no means of forming a very definite opinion as to 
how she will séay under low sail in a sea-way, how she will wear, how scud 
in a following sea, or how stand up under her sails, or whether her statical 
stability be too much or too little, or how the fore and after bodies are 
balanced. These are points to be determined, not by the mere opinion of 
seamen—-for a sailor will vaunt the qualities of his ship even as a lover the 
charms of his mistress—but by careful records of performances in smooth 
water and at sea, and a comparison of such performances with calculated 
results from drawings beforehand. Let a return of such things be annually 
laid before the House of Commons—we shall then know whether we are get- 
ting money’s worth for our money; and also we should receive all the benefits 
of public criticism towards improvement. We should not then allow defects 
to be stereotyped, till chronic blemishes are turned into beauties, or, if not 
so, then defended as things that cannot be remedied. 

I have now completed the task which four years ago I imposed on myself. 
Beginning with simple elementary principles, and ending with minute prac- 
tical details, I have, as I conceive, shown the process by which the improve- 
ment of steam-ships must be carried on. 

More than one hundred years ago scientific men, able mathematicians, 
showed the physical laws on which naval architecture must rest. A succes- 
sion of able men have shown how those laws affect various forms of floating 
bodies. Experiments have been made with models to determine the value 
of the resistance practically. With the exception of some experiments of 
Mr. Scott Russell, I am not aware that any have been made with vessels ap- 
proaching the size of ships to determine the relations of resistance to power, 
whether wind or steam. 

Ships have been improved, and modifications of form have been arrived at 
by along painstaking tentative process. The rules so reached for sailing ships 
have been superseded by steam, and we are still following the same tedious 
process, in order to establish new rules for the application of steam power. 

I think the history of naval architecture shows that it is not an abstract 
science, and that its progress must depend on the close observation and cor- 
rect record of facts; on the careful collating, and scientific comparing of such 
facts, with a view to the induction of general laws. Now, is there any where 


such observing, recording, collating, and comparing? and still more, is there 
such inducting process ? 


174 REPORT—1860. 


I can find no such thing anywhere in such shape that the public can judge 
it by its fruits. 

We are now in full career of a competition of expenditure, and England 
has no reason to flinch from such an encounter, unless her people should tire 
of paying a premium of insurance upon a contingent event that never may 
happen ; and if it should happen without our being insured, might not cost 
as much as the aggregate premiums. ‘Tire they will, sooner or later, but 
they are more likely to continue to pay in faith and hope, if they had some 
confidence that their money is not being spent unnecessarily. 

There is now building at Blackwall the ‘ Warrior,’ a ship to be cased with 
44-inch plates of iron, whose length at water-line is 380 feet, breadth 58 feet, 
intended draught of water (mean) 255 feet, area of section 1190 square feet, 
and displacement about 8992 tons, and she is to have engines of 1250 nomi- 
nal horse-power. 

Is there any experience respecting the qualities and performance of such 
a ship? Anything to guide us in reasoning from the known to the unknown ? 
Do the performances of the ‘ Diadem,’ ‘Mersey,’ and ‘Orlando,’ inspire 
confidence? Where are the preliminary experiments ? 

Before any contract was entered into for the construction of the Britannia 
Bridge, a course of experiments was ordered by the Directors, which cost not 
far short of £7000, and it was well expended. It saved money, and perhaps 
prevented failure. This ship must cost not less than £400,000, and may cost 
a good deal more when ready for sea. But there is another of similar, and two 
others building, of smaller size. What security is there for their success ? 

The conditions which such a ship as the ‘ Warrior’ must fulfil in order to 
justify her cost are deserving of some examination. The formidable nature 
of her armament, as well as her supposed impregnability to shot, will natu- 
rally lead other vessels to avoid an encounter. She must therefore be of 
greater speed than other ships of war. To secure this, it is essential that 
her draught of water should be the smallest that is compatible both with 
stability and steadiness of motion, and that she should not be deeper than the 
designer intended. ‘To ensure steadiness it is necessary, among other things, 
that in rolling, the solids, emerged and immersed, should find their axis in 
the longitudinal axis of the ship. To admit of accurate aim with the guns, 
her movement in rolling should be slow and not deep. Every seaman knows 
how few ships unite these requisites. 

It is not quite safe to speculate on the ‘ Warrior's’ speed; nevertheless I 
will venture on an estimate, such as I have stated in the case of the ‘ Great 
Eastern,’ whose smooth-water speed I will now assume to be 152 knots, as 
before estimated, with 7732 horse-power, when her draught of water is 23 
feet, her area of section, say 1650 square feet, and her displacement about 
18,588 tons. The speed of the ‘ Warrior’ in smooth water ought not to be 
less than 16 knots, in order that she may force to action unwilling enemies 
whose speed inay be 13 to 14 knots. 

The question I propose is the power to secure a smooth-water speed of 
16 knots. 

Reducing the ‘ Great Eastern’ to the size of the ‘ Warrior,’ and applying 
the corrections for the difference of speed of 3 knot, and for their respective 
coefficients cf specific resistance °0564 and ‘07277, the horse-power for 16 
knots is 7543. 

Raising the ‘ Niagara’ to the size of the ‘ Warrior,’ and applying the cor- 
rections for the difference of speed between 10°9 and 16 knots, and for their 
respective coefficients of specific resistance ‘0797 and ‘07277, the horse-power 
to give the ‘ Warrior’ a smooth-water speed of 16 knots is 7867, being an 
excess over the estimate from the ‘Great Eastern’ of 324 horse-power. 


ON THE EFFECTS OF LONG-CONTINUED HEAT. 175 


If the power required for the ‘ Warrior’ be calculated by adaptation from 
the ‘ Mersey’ and the ‘ Diadem,’ it would be 8380 horse-power and 8287 re- 
spectively ; from which this inference flows :—that unless the mistakes made 
in the fore and after sections of the ‘Mersey’ and ‘Diadem’ are rectified in the 
‘Warrior,’ she will require above 8000 horse-power for a speed of 16 knots, 
notwithstanding her greater size and increased ratio of length to breadth. 

Before investing more than a million and a half of money in an experiment, 
commercial men would have probably employed a few thousand pounds in 
some sort of test as to the conditions of success. Perhaps such test may have 
been resorted to and kept secret for reasons of public policy. Perhaps it is 
intended that the ‘ Warrior's’ speed should not be greater than that which is 
due to five times her nominal horse-power, which could not exceed 152 knots 
with 6250 horse-power, under the most favourable conditions, and may be 
much less. 

The British Association, by becoming the medium of collecting facts and 
presenting them to the public, has done good service; but that service ought 
not to rest there. Collectively, the Association may be able to do little more. 
It can only act by affording public opinion a means of expression. But indi- 
vidual members may do much. Towards such opinion I am doing my part. 

I ask, in the cause of science, what is the system under which the Queen’s 
ships are designed and their steam power apportioned ; the organization by 
which their construction and fitting for sea are carried on; the supervision 
exercised over their proceedings at sea, in the examination of returns of per- 
formance and of expenditure ? 

During part of 1858 and 1859, two committees appointed by the Admi- 
ralty collected evidence and made reports on the Dock Yards and on steam 
machinery. I have read both reports with some attention. They are not 
conclusive, but they are entitled to respect. I have also read the replies and 
objections of the Government officers. There is a clear issue between them 
on some of the most essential principles of effective economical management, 
and on the application of science. 

A Royal Commission has been appointed to inquire into the system of 
control and management in the Dock Yards. This is so far good, but it 
does not go far enough. It does not comprise the steam machinery reported 
on by Admiral Ramsay’s Committee, and it cannot enter upon the questions 
Ihave just enumerated. Yet the efficiency of the fleet depends quite as 
much upon the adaptation of the machinery to the ship, and of the ship to 
the use she is to be put to, as it does upon the manner in which she is built. 
The Commission ought to be enlarged both in objects and in number of 
members. It consists of five members only. 


Report on the Effects of long-continued Heat, illustrative of Geological 
Phenomena. By the Rev. W. Vernon Harcourt, F.B.S., F.G.S. 


Tue chief occupation of those who during the present century have 
employed themselves in investigating the history of the earth, has been to 
develope the succession of its strata. In following this pursuit, they have 
found their best guide in the study of its organic antiquities, and have not 
been led, for the most part, to very precise views of the physical and chemi- 
cal changes which it has undergone. 

Yet there are questions in Geology to which no answer can be given with- 
out an accurate examination into these. In regard, for example, to the 


176 REPORT—1860. 


chronology of the earth, the observation of organic remains alone can never 
supply reliable data for reasoning. If we should attempt to draw inferences 
from biological analogies, and measure the duration of beds by the growth of 
imbedded skeletons, we should be stopped by the probability that the first 
species of every series were successively created in a state of full-grown 
maturity*, and by the intrinsic weakness of all comparisons instituted non 
part materia. 

Neither can any precarious mechanical analogies render the inquiry more 
definite, or give a logical value to our conclusions. We are not entitled 
to presume that the forces which have operated on the earth’s crust have 
always been the same. Were we to compare the beds of modern seas and 
lakes with the ancient strata, and assume proportionable periods for their 
accumulation, we must assume also that chemical and mechanical forces 
were never in a state of higher intensity, that water was never more rapidly 
evaporated, that greater torrents, fluid or gaseous, never flushed the lakes and 
seas, and that more frequent elevations and depressions never gave scope for 
quicker successions of animal life. To gain any real insight into these ob- 
scure pages of ancient history, we must have recourse to a strict induction 
of physical and chemical facts, and thence learn the probable course, and 
causes, of the wonderful series of changes which geology unfolds. 

I am not aware that any full and connected statement has been published 
of the facts which have been contributed by physical observations, and 
chemical experiment, towards elucidating the conditions of those changes, 
and propose therefore to preface the account which I have to give of experi- 
ments designed to throw light upon them, with a sketch of the progress of 
science in that department. 

Forty years have elapsed since the author of the ‘Mécanique Céleste’ 
drew attention to the fact that multiplied observations in deep mines, wells, 
and springs, had proved the existence of a temperature in the interior of the 
earth increasing with the depth. He remarked that, by comparing exact 
observations of the increase with the theory of heat, the epoch might be 
determined at which the gradually cooling globe had been first transported 
into space ; he stated the mean increase, collected from actual data, to be a 
centesimal degree for every 32+ metres, and added that this is an element 
of high importance to geology. ‘ Not only,” he said, ‘‘does it indicate a very 
great heat at the earth’s surface in remote times, but if we compare it with 
the theory of heat, we see that at the present moment the temperature of 
the earth is excessive at the depth of a million of metres, and above all at 
the centre; so that all that part of the globe is probably in a state of fusion, 
and would be reduced into vapour, but for the superincumbent beds, the 

* To suppose otherwise with regard to animals which take care of their young would be 
absurd; and hence it is probable also that this is the general system of creation. The most 
remarkable fact which modern geology has disclosed is the continual succession of newly- 
created species. It has been attempted to account for thes2 according to known laws of pro- 
geniture, by supposing numerous non-apparent links of transitional existence to fill up the 
gaps in the chain of derivation by which one species is presumed to have descended from 
another. But this is only twisting a rope of sand; conjectural interpolations cannot give 
coherence to a set of chains which are destitute of all evidence of continuity one with 
another, and between which, as far as our experience goes, Nature has interposed a prin- 
ciple of disconnexion. 

In using the word creation, we acknowledge an agenf, and own our ignorance of the 
agency, with regard to which, in this case, we only know that it is systematic ; for we see 
successive species accommodated to successive conditions of existence. 

+ M. Babinet (Tremblements de Terre, 1856), taking M. Waiferdin’s measurement from 
artesian borings, which gave 31 metres for ]° C. as the most exact, remarks, that the tem- 
perature at the depth of 3 kilometres must be above the heat of boiling water, and at that 
of 60 kilometres, about 2000° C., sufficing for the fusion of lava, basalt, trachyte, and 
porphyry. 


ON THE EFFECTS OF LONG-CONTINUED HEAT. 177 


pressure of which, at those great depths, is immense.” ‘ These considera- 
tions,” he further added, “ will explain a great number of geological phe- 
nomena ;” and he instanced those of hot springs, which he accounted for on 
the supposition that rain-water in channels communicating from super- 
ficial reservoirs with the interior of the earth, thence rises again, heated, 
to the surface. 

Fourier, at the same time, expounded the methods by which, after extended 
observation of the internal temperature, and further experiments on the 
conduction of heat, he conceived that mathematic analysis might determine 
the epoch at which the process of cooling began, concluding in the mean- 
while from facts already known,—Ist, that no sensible diminution of tem- 
perature has taken place during the period of historical chronology ; 2ndly, 
that at a former era the temperature underwent great and rapid changes. 

Thus was a train of graduated causes, physical and chemical, introduced 
into Geology on the foundation of inductive reasoning, which is capable of 
resolving some of the chief difficulties of the science in our comparison of 
the present with the past. 

When, for instance, we read in the organic contents of the strata the 
history of a period when the climate was apparently uniform in all parts of 
the earth, and learn from the imbedded plants that the temperature of Arctic 
lands was once equal to that of warm latitudes at the present day, to account 
for these circumstances, we need no longer bewilder ourselves with hypo- 
theses ; we have a vera causa in the knowledge that the earth has passed 
through a state in which its temperature was due, not so much to a sun then 
veiled in clouds, as to a heat penetrating equally in all directions from the 
centre to the circumference of the globe. 

When, again, we contemplate a mountain range, and view the abrupt pre- 
cipices of some alpine chain, with its enormous masses of rock uplifted to 
- the clouds, and descending as many miles into the bosom of the sea, and 
when we compare such abnormal labours of nature with the petty risings 
of the earth’s surface in the existing state of things, we have a vera causa 
for that disparity, in the knowledge that there was a time when the eruptive 
forces of the seething mass within were greater, and when a weaker crust 
underwent vaster disturbances. 

Or if we examine the general structure of the strata, and see the same stra- 
tum contemporancously solidified over large portions of the earth’s circum- 
ference, and then observe the absence of consolidation in the actual opera- 
tions of nature, whether under the pressure of deep seas, or elsewhere, 
except in a few foci of igneous action, we have here also a vera causa 
of the difference, in the ancient prevalence of that high temperature which 
the laboratory of nature and art shows to be the most capable of lapidifying 
stony materials. 

Descending into the details of mineralogy, we find the same departure 
from the present order of nature in the constitution of minerals; and in the 
sequence of chemical effects of heat increasing with the age of the stratum, 
we see a real cause for the distinction. 

Thus, for example, to begin with the upper beds; the chemist knows that 
solutions of carbonate of lime, at the ordinary temperature, deposit crystals 
with the common form of calcareous spar, but near the boiling-point of 
water with that of drragonite. Now in the mineralogical collection of the 
Yorkshire Philosophical Society is a specimen of this mineral investing 
calcite, from the chalk cliffs of Beachy Head ; and if any one will examine the 
caves of calcareous grit on the Yorkshire coast, he will find them in some 
aie like those of volcanic rocks, or the mouths of hot springs, with 

. N 


178 REPORT—1860. 


Arragonite*. Here then we have proof of a certain modicum of heat existing 
in boiling-springs now extinct, which once pervaded these strata; for had the 
heat of the water which left this deposit been much more, or less, than about 
212° F., no such crystals could have been formed. Not far from the same 
locality, in a thin seam of the cornbrash Oolite, I have found nodules en- 
closing small Crustacea, the interior of which was filled with crystalline 
blende. No other trace of zinc is to be seen in the country aroundt. The 
same singular phenomenon may be observed in the neighbouring Lias-shale, 
where the chambers of the Ammonites frequently contain blendet. This is 
not a phenomenon peculiar to the district ; it illustrates the general con- 
dition of the-earth after these shells were deposited, and is best accounted 
for by the vera causa of an elevated temperature ; it indicates that the fumes 
of zine, or one of its volatile combinations, must have penetrated the strata, 
taking the form of blende in the chambers of the Ammonite, and having 
been sealed up in these, escaped decomposition. 

The same account is applicable to the dissemination of carbonate and sul- 
phide of lead and copper in the Permian and Triassic strata, and of the 
particles of metallic copper in the mountain limestone ; as well as to the de- 
posits of calamine in the hollows of that rock, on the conditions of which de- 
posits light is thrown by an experiment of Delanoue, who found that no pre- 
cipitate of carbonate of zinc is produced by limestone at the common tempera- 
ture, but that it is perfectly thrown down from a warm solution of its salts. 

And here also it is worthy of remark, that in the experiments of Forch- 
hammer to illustrate the formation of dolomitic strata, when a solution of 
carbonate of lime was mixed with sea-water at a boiling heat, the compound 
formed contained only 18 per cent. of carbonate of magnesia, but that the 
proportion of magnesia increased with an increase of temperature; in the 
experiments of Favre and Marignac, the composition of equal atoms, which 
is that of many natural beds of magnesian limestone, was attained by raising 
the heat to 392° F., and the pressure to 15 atmospheres; and in those of 
Morlot a mixture of sulphate of magnesia and calcareous spar was com- 
pletely converted, in the same circumstances, into a double salt of carbonate 
of lime and magnesia, with sulphate of lime. 

The probable history of all the caleareous and magnesian strata, with 
their interstratified cherts and flints, and interspersed chalcedonie fossils, is 
that they are products of submarine so/fataras, whence issued successively, 
in basins variously extended, gases and springs capable of dissolving pre- 
existent beds, which caused alternate depositions .of silica and carbonated 
earths, and intermitting from time to time, allowed intervals for the succession 
of organic and animated beings. 

The manner in which materials are furnished for extensive sedimentary 
deposits by processes of disintegration dependent on subterraneous ema- 
nations, has been observed by Bunsen in the solfataras of Iceland. He 
describes the palagonitic rocks, formerly erupted there, as undergoing con- 

* Dr. Murray informs me that this Arragonite is found in a little bay within six miles of 
Scarborough, in the seams and crevices of the upper calcareous grit. He describes it as 
fibrous, compact, or imperfectly mammillated, wanting the oblique cleayage of calcite, 
scratching Iceland spar, and flying into powder in the flame of a taper. Mr. Procter having 
at my request taken the specific gravity of a fibrous specimen, finds it 3, and confirms Dr. 
Murray’s description of the other characters of this mineral. 

+ The only peculiarity is that a basaltic dike traverses the district at a distance of a few 
miles from the site of the fossils. 

t The Lias fossils sometimes also contain galena. Blum describes a bivalve from a fer- 
ruginous oolitic rock near Semur, the shells of which consist entirely of crystalline lamin 
of specular iron; and a cardinia from the lower lias, according to Bischof, likewise consists 
of the same mineral, which we know elsewhere as a result of volcanic action. 


Le 


ON THE EFFECTS OF LONG-CONTINUED HEAT. 179 


version by these means “ into alternate and irregularly penetrating beds of 
white ferruginous, and coloured ferruginous, fumerole clay, the deposits 
being disclosed to a considerable depth, and exhibiting in the clearest man- 
ner the phenomena of alternating colours.” ‘‘ One is astonished,” he re- 
marks, “ at observing the great similarity between the external phenomena 
of these metamorphic deposits of clay still in the act of being formed, and 
certain structures of the Keuwper formation. Thousands of years hence the 
geologist who explores these regions when the last traces of the now active 
fumeroles have vanished, and the clay formations have become consolidated 
into marl-like rocks by the silica with which they are saturated, may suppose, 
from the differently stratified petrographic and chemical character of these 
beds, that he is looking at fletz strata formed by deposition from water.” 
*« At the surface, especially, where the deposition is favoured by slow eva- 
poration, innumerable crystals of gypsum, often an inch in diameter, may 
frequently be observed loosely surrounded by an argillaceous mass. At the 
mountain ledge of the Namarféyall, and at Krisuvik, this gypsum is found 
to penetrate the argillaceous masses in connected strata and floor-like depo- 
sits, which not unfrequently project as small rocks where the lower soil has 
been carried away by the action of the water. These deposits are sometimes 
sparry, corresponding in their exterior very perfectly with the strata of gyp- 
sum so frequently met with in the marl and clay formations of the Tras.” 

The great disturbances and fractures, the trappean rocks, and the frag- 
ments of porphyritic conglomerates, at. the bases of these formations, tend to 
confirm the opinion of Bunsen, that they have had a metamorphic origin, an 
origin very probably common to other beds, whether consisting of marl, shale, 
or sand. All the sand-beds now forming are due to the disintegration and 
detritus of ancient sandstones, a process, which continued through a great 
lapse of time, has but coated some portions of the sea-side with unconsoli- 
dated sand. In the soundings of the Atlantic depths, the microscope, according 
to Maury, has failed to detect a single particle of sand or gravel. For the 
origin and consolidation of the inferior grits and shales we must look to ac- 
tions, mechanical and chemical, more potent than those which the present 
tranquil course of nature presents. In examining the carboniferous sand- 
stones of the Blue Mountains in New South Wales, with their shales and coal- 
beds, more than 12,000 feet in thickness, Darwin was ‘“‘surprised at obser- 
ving, that though they were evidently of mechanical origin, all the grains of 
quartz in some specimens were so perfectly crystallized that they evidently 
had not in their present form been aggregated in a preceding rock;” and 
he quotes Wm. Smith as having long since made the same remark on the 
millstone grit of England. If any one, in fact, will observe with a lens the 
surfaces of the quartz pebbles included in that grit, he will find on most of 
them numerous wnabraded facets, which bear evidence of a quartz-crystalline 
action having pervaded the rock whilst its consolidation was going on. 

There can be no better proof of widely-spread chemical action due to 
heat than the frequent presence of crystallized silica in every part of the 
stratified rocks. 

The deeper we descend in the strata, the more plentiful are the veins and 
beds of guartz, and the more manifest the signs of metamorphic action. 
Von Buch was the first to explain, on the principle of metamorphism, 
the change of calcareous rocks, in contact with pyroxenic porphyries, into 
dolomites ; and in 1835 the same principle was extended by Fournet to 
the metallization of rocks by contact with quartziferous porphyries, and to 
their felspathication and silicification by the contact of granite. “Since 
the theory of a central fire,” he observed, “has been confirmed by modern 
researches, all the great questions in the history of the globe appear suscep- 

N2 


180 REPORT—1860. 


tible of a simple solution, and it is astonishing that chemists have not yet 
carried their views in this direction. From the moment that we consider the 
terrestrial globe as a mass of which the different parts have successively 
undergone the action of fire, we must also conceive, as a necessary conse- 
quence, a series of chemical phenomena, such as calcination, fusion, cemen- 
tation, &c.,” meaning by this latter term, the mutual molecular inter- 
penetration of bodies in contiguity, a process of which I shall presently have 
to offer a remarkable example. 

There was one mineralogical chemist, however, of high eminence, who had 
long before carried his views in the direction desired by Fournet. In 1823, 
Mitscherlich, having examined the forms, and analysed the ingredients, of 
forty crystalline products of furnaces *, to which Berthier had contributed 
several parallel results of experimental processes, pronounced them identical 
with various native minerals, and in particular with peridot, pyroxene, and 
mica. In the artificial mica, however, he found Lime, of which granitic 
mica scarcely contains a trace; and this led him to speculate on the cause 
of the chief chemical distinction between the granite and trap formations, 
consisting in the absence of calcareous and magnesian silicates from the 
former. Supposing, he argued, that the primary rocks were formed at that 
stage of the earth’s refrigeration when 4ths of its water were in a state of 
vapour, the pressure on every part of its surface, computed according to 
Laplace’s calculation of the mean depth of the sea, would be 225 atmo- 
spheres + ; but under such a weight the affinity of lime for silica would cease ; 
hence the crystals of uncombined silica in Carrara marble. 

The surmise has since been brought into evidence by an experiment of 
Petzholdt, in which pulverized quartz, heated to whiteness with an equal 
weight of carbonate of lime in an open vessel, was found to form a silicate 
with the lime, but produced no combination when heated in a strong, close 
vessel of iron. 

The crystallization of the primary rocks was supposed by the early Plutonic 
theorists to be due to slow cooling ; but this principle alone does not satisfy 
the phenomena. The crystalline structure of granite is seen, for example in 
Glen Tilt, at Shap Fell}, and elsewhere, to be equally uniform in its partial 
irruptions into the superior strata, as where it appears to be the foundation 
stone of the earth's crust; it has crystallized in its accustomed manner, where 
it has penetrated fissures of the upper beds in plates as thin as the leaves of 
a book and threads as fine as a hair, and even where it is involved in the in- 
vaded stratum so that no junction with any vein can be observed. How 
could it have been thus injected in a state of fusion, unless of the most liquid 
kind? and how could the heat of such liquidity, in a material of which the 
fusing-point is so high, be otherwise than rapidly cooled down? 

Furthermore, the quartz which forms su large a constituent of granite, 
has always the specific gravity of crystalline silica, which exceeds that of any 
other species of silica. But Deville and others have shown that fusion 


* Annales de Chimie, tom. xxiv. p. 258, 1824. Mitscherlich sur la production artificielle 
des minéraux crystallisés—“j’ai trouvé, 4 Fahlun, du silicate et bisilicate de protoxide de 
fer, 2 Garpenberg, du mica et du pyroxene, les mémes figures crystallines, et tous les autres 
caractéres des minéraux correspondans, le bisilicate de protoxide de fer et de chaux, de 
magnésie et de chaux, les trisilicates de chaux, de chanx et de manganése, le fer oxidé (fer- 
rosoferricum), le protoxide de cuivre, le deutoxide de cuivre, ]’oxide de zinc, les sulfures 
de fer, de zine, de plomb, l’arsénieure de nickel, &c. &c., et beaucoup d’autres substances 
en cristaux bien prononcées. 

t In Mitscherlich’s Mémoire, as printed in the ‘Annales de Chimie et de Physique,’ 
tome xxiv. pp. 372, 373, the atmospheres are stated as 2250, deduced from a mean depth of 
sea, 96,000 feet, with a cipher too much, that is, in both cases. 

¢ I understand from Mr. Marshall that the ramified granite of Shap Fell is similarly 
crystallized with the rest of the rock, but finer grained. 


ON THE EFFECTS OF LONG-CONTINUED HEAT. 181 


lowers this specific gravity to a constant amount, and that fused silica does 
not recover its density in cooling. Crystalline granite, as Delesse has shown, 
passes by fusion from the density of 2°62 to that of 2°32, and Egyptian 
porphyry from 2°76 to 2°48. . 

Again, the felspar in granite is encrusted by the quartz, the most fusible 
by the least fusible material, contrary to all experience of crystallization 
either from solution or fusion. 

Lastly, all the minerals of which granite is composed have been artificially 
produced, and their production has in every instance taken place at tempera- 
tures far below that of the fusing-point of that rock. ‘The first specimens 
of artificial felspar analysed by Karsten, and measured by Mitscherlich, 
were found in the lining of a copper furnace amongst a sublimate of zinc. 
Mitscherlich tried to obtain the like by fusing several pounds of native felspar 
in a porcelain furnace, and subjecting the mass to a process of slow cooling, 
but without success*. In the Mulden sinelting works, Cotta observed the 
walls of the furnace traversed, in the joints of its masonry, and in the cracks 
which it had undergone, by beautiful metallic veins, the sides exhibiting the 

_phenomena of impregnation and alteration as in the boundary walls of 
natural veins, and the ores consisting of galena, blende, iron and copper 
pyrites, purple copper, Fahl ore, native copper, &c. In like manner pyro- 


morphite (Pb’ P+4+4 Pb Cl), in well-formed six-sided prisms from the iron 
furnace at Asbach, was found attached to the stones of the masonry. There 
can be no doubt but that Karsten’s crystals of felspar, like these, were 
formed by gaseous sublimation; and an analogous process would account 
for the felspar observed by Haidinger in a basaltic cavity, under the form 
of Laumonite, and by Bischof in a porphyritic bed, in which a Trilobite 
also was found. 

A new view of the production of minerals has been opened by Ebelmen, 
who obtained the most refractory crystals of the granitic rocks, such as 
spinel, emerald, cymophane, and corundum, by segregation in the interior 
of a fused mass. They were formed at a heat far below that which would 
fuse either those crystals or granite, by means of the evaporation of a fusible 
and volatile medium. Gaudin also, on the same principle using a similar 
alkaline solvent, and substituting sulphuric for boracic and carbonic acids 
as the volatile ingredient, obtained the ruby. 

To the same category may be referred an experiment by Precht, who 
having added to a transparently fused frit, weighing 14 ewt., a considerable 
quantity of felspar, found, after cooling, that a large portion of this mineral 
had separated itself in foliated masses, and in several distinct crystals. 

The most important light, however, on this subject, especially in relation to 
metamorphic phenomena, is from the experiments cf Daubrée on the reaction 
of gaseous compounds upon various earthy bases. Conveying the chlorides 
of tin and titanium over lime at heats varying from 572° to 1652° Fahr., 
he produced crystals of tinstone and brookite; by variations of the same 
principle, at heats not exceeding redness, he obtained all the following mine- 
rals :—wollastonite, staurolite, peridote, disthene, willemite, idocrase, garnet, 
phenakite, emerald, euclase, corundum, zircon, periclase, spinel, augite, di- 
opside, gahnite, franklinite, hematite, felspar, and tourmaline in hexagonal 
prisms imbedded within crystals of guartz. The process was of this descrip- 
tion :—Chloride of aluminium, passed over lime at a red heat, produced 
corundum; chloride of siliciwm, passed in like manner over seven equiva- 
Jents of potash or soda and one of alumina, produced the different species 
of felspar : the latter named gas, decomposed by lime at the same heat, or 


* Mr. Marshall fused a large mass of granite, and cooling it slowly obtained no crystals. 


182 REPORT—1860. 


by magnesia, alumina, or glucina, gave erystallized quartz in the usual form 
of the pyramidal hexagon, passing below into a silicate of the associated 
bases. ‘“ The most remarkable part,” as Daubrée has remarked, “ connected 
with these reactions, in a chemical, and especially a geological point of view, 
is that the silicium and the silicates thus produced have an extreme tendency 
to crystallize, and that the crystallization takes place at a temperature far 
below their points of fusion.” “* The manner,” he adds, “in which quartz and 
the silicates are connected with the granite rocks has long been a difficulty 
in all the hypotheses on the formation of the rocks called primitive. Now 
we find, in our experiments, that guartz crystallizes at the same time with, 
or even later than, the silicates at a temperature scarcely exceeding a cherry- 
red heat, and consequently infinitely below its point of fusion.” 

M. Daubrée disclaims the supposition that those rocks themselves were 
formed after the formula of his experiments. Nevertheless, considering 
the probability that formations at higher temperatures, now obliterated, may 
have preceded that of the granitic rocks, observing the uniform erystalliza- 
tion of granite in the tenuity of its ramifications, as well as in mass, and 
perceiving that Daubrée by his process has reproduced almost all the granitic 
minerals, and among them not only the felspar, but the crystalline quartz 
of granite,—it must be admitted that such a theory is worth attention. 

Durocher has added to Daubrée’s researches two capital experiments, of 
direct geological application, in obtaining the sulphides of the mineral veins 
by the reaction of sulphuretted hydrogen on the chlorides of the metals in a 
state of vapour, and in having effected the metamorphism of limestone into 
dolomite in an atmosphere of the vapour of chloride of magnesium. 

A theory of sublimation, however, may admit of many modifications, 
and may be combined with the principle of segregation illustrated in the 
experiments of Ebelmen. Deville and Caron, having fused bone phosphate 
at a red heat in excess of chloride and fluoride of calcium, found that lime 
apatite crystallized out in cooling, and was easily separated by washing from 
the soluble salts. In like manner, with different bases and different chlorides, 
they obtained the numerous varieties of apatite and wagnerite. And they 
observed further, that all these minerals became volatile at a slightly elevated 
temperature in the vapour of the chloride amidst which they were formed. 

Senarmont, pursuing another course, had applied a heat somewhat ex- 
ceeding 662° Fahr. toan aqueous solution of hydrochlorate of alumina, con- 
fined in a close tube, and thus decomposing it into its volatile and solid 
ingredients, obtained corundum, distinctly crystallized and mixed with 
diaspore, the same substance under a different form, and with different 
chemical properties, thus repeating in a remarkable manner that process by 
which the same minerals are found in nature similarly intermingled. He 
also succeeded in eliminating crystals of quartz from hydrate of silica by 
dissolving the hydrate in water charged with carbonic acid, and gradually 
raising the temperature of the tube which contained it to a heat of from 
400° to 500° Fahr., and by analogous methods he obtained carbonates and 
sulphides identical with native minerals. In some of these experiments the 
process was so varied as to show that the separation of the anhydrous cry- 


stals was due to the gradual withdrawal of the dissolving gas. The hydrated © 


sesquioxide of iron, also heated in water of the temperature of 360° Fahr., 
was dehydrated, becoming magnetic. In an experiment by Wéhler, on the 


contrary, apophyllite dissolved in water at the same temperature, returned — 


on cooling to its original form, retaining its water of crystallization. To this 
class of discovery Daubrée has likewise added some valuable facts, having — 


obtained regular crystals of quartz, by decomposing, with the vapour of — 


water alone, the interior of a glass tube subjected to a low red heat ; at the 


¥ 


2 


ON THE EFFECTS OF LONG-CONTINUED HEAT. 183 


same time silicates were formed, hydrated or anhydrous, according to the 
degree of heat; when fragments of obsidian were inserted, crystals of 
Rhyacolite appeared ; and the silicated water of Plombiére being substituted 
for plain water, and kaolin for obsidian, crystals of diopside insinuated 
themselves into the silicated substance of the tube, and the kaolin was 
changed into a substance possessing felspathic characters. 

All these experiments are adverse to the idea that the primary rocks have 
undergone fusion. The best natural criterion, perhaps, of the temperature 
at which they were formed, was afforded by the discovery, in 1828, of a 
method of manufacturing wltramarine, based on Vauquelin’s identification 
of a furnace-product with the Lapis lazuli found in granite and in primitive 
limestone. In some specimens which I possess of the latter rock, this 
beautiful mineral may be seen enamelling with minute specks, and with 
perfect distinctness, within and without, all the plates of the calcareous 
erystals, which are here and there interspersed with small crystals of sulphate 
of lime. The heat at which the artificial ultramarine is made is that of red- 
ness. A lower temperature will not suffice to produce the colour, and a 
higher destroys it. 

We can now better understand how Hunterite, a white felspathic mineral 
containing 11°6 per cent. of water, can have been formed where it is found ; 
a hydrated silicate of alumina in the bosom of molten granite is an anomaly 
for which high pressure would scarcely account; but if the rock was at the 
temperature only of a low red heat, the formation of this mineral, and of 
the hydrated micas, will no longer appear a marvel. 

Other notices of ancient degrees of heat have been observed in the 
strata. In a cavity within a quartz crystal from Dauphiné, Davy founda 
viscous inflammable fluid in small quantity, in a perfect vacuum*. In the 
cavities of other quartz crystals he found water and rarefied air. Sorby, 
having determined the amount of rarefaction in one such from a bed of 
mica-slate, in which he detected many others, calculated the temperature of 
the crystal at the time of its formation to have been 320° Fahr. In one case 
Davy found evidence of pressure which had condensed the elastic fluid in a 
erystal of quartz, and Brewster observed the like in crystals of topaz. 

From a general review of the researches now detailed, the following infer- 
ences may be drawn :— 

1. That all the consolidated strata, viewed chemically, bear marks of sub- 
jection to an action of heat agreeable to the theory of the earth’s refrigera- 
tion, in direct proportion to the age of their deposit ; and that they show that 
action most explicitly in the presence, throughout, but more abundantly as 
the series descends, of that peculiar form of silica which is chemically repro- 
duced by the action of heated volatile matter. 

2. That the igneous minerals were formed by molecular aggregation, at a 
heat not exceeding, perhaps, that of an ordinary fire, either as a residuum 
from the expiration of fusible and volatile materials, or more generally as a 
deposit from volatile forms of matter. 

As there are two classes of eruptive rocks, the guartzose and unquartzose, 
so there are two classes of emanation which accompany them, and deposit 
earthy minerals, differing for each class, in the neighbouring strata. They 
generally mantle round the rock, and but seldom penetrate it; as if it had 
rather made room for them to rise, than as if they made part of its substance. 
Yet they bear a resemblance to the character of the rock which they follow. 
Thus the erystallized owide of silicon is the characteristic ingredient of granite 


* Rose quartz from granite, and cornelian from trap, are coloured by a carburet of hydro- 
gen; crystals of graphite also have been found in quartz; but as carbonic acid must have 
existed before plants could grow, these facts are no proofs of antecedent organic structure. 


184 REPORT—1860. 


rocks; and the earthy minerals imbedded in the metamorphic strata around 
such rocks resemble quartz in being simple crystallized oxides,—innumerable 
gems, for instance, of the crystallized oxide of alumina—vast masses of the 
same, many tons in weight, in the form of emery, encysted in limestone 
which has been metamorphosed by rocks of granitic character,—still greater 
masses of crystalline sesquiowide of iron in similar relation to those rocks,— 
crystalline peroxide of tin shot through them into the strata above. 

In the eruptive rocks which followed the guartzose, these minerals, with 
almost all the quartz, died out, and were succeeded by others of a more 
complex nature appropriate to the porphyritic, trachytic, basaltic, and lavie 
eruptions. Yet all these, as well as the granitic, are attended by similar 
metalliferous veins, which grow very weak in the latest, but still show, at least 
as far as the eruption of the more ancient lavas*, a continued communica- 
tion with a common reservoir deeper seated than any of them. 

Davy saw the lava of Vesuvius issuing, as if forced up by elastic fluids, 
perfectly liquid, and nearly white-hot, its surface in violent agitation, with 
large bubbles rising from it, which emitted clouds of white smoke, consisting 
of common salt in great excess, much chloride of iron, and some sulphate of 
lime, accompanied with aqueous vapour, and with hydrochloric and sul- 
phurous acids. It contains also realgar and sulphide of copper, due pro- 
bably to the reaction of sulphuretted hydrogen on the chloride of the metal. 

In the early time of these eruptive emanations, when they escaped at 
many points with little interruption, the land rose only to low levels above 
the waters. As the crust of the earth grew more solid and weighty, and 
the vent was confined to fewer lines of shrinkage, the elastic elements of 
disturbance upheaved the incumbent beds with greater power, and the 


* Though the presence of quartz in lava has been denied, the following account of its 
coexistence with schorl in that of the valley of Maria in Lipari by Spallanzani shows that it 
does exist in ancient, perhaps basaitic, lavas, and strikingly illustrates the theory of its sub- 
limation, as here advanced. ‘‘ Among the lavas partly decomposed we find pumices and 
enamels containing felspars and scales of black schorls, and certain curious and beautiful 
objects, which derive their origin, in my opinion, from filtration. The lava is white and friable 
to a certain depth, of a petrosiliceous base, full of small cells and cavities, within which these 
objects make their appearance :—Tirst, minute crystals of schorl ; from the inside of these 
cells project very slender schorls, sometimes resembling minute chestnut bristles, sometimes 
a bunch, a plume, or a fan, to be ascribed to filtration after the hardening of the lava, since 
though it is common to find schorls in lavas, they are found incorporated within them, not 
detached as in this case. The second filtration has produced small guartzose crystals, and 
the manner of their distribution in prodigious numbers renders them a very singular phe- 
nomenon among volcanic objects. Wherever the lava is scabrous, wherever it has folds, 
sinuosities, cavities, or fissures, it is full of these crystallizations. The larger crystals extend 
to 34 lines, the greater part about 4a line. They consist of a hexagonal prism, infixed 
by the base into the lava, and terminated by a similar pyramid. Three crystals, among those 
I examined, were terminated by two pyramids, the prism being attached to the lava by a 
few points, and the prisms projecting out. The most regular are in small cavities, but not 
a few are on the surface of the lava. The Java, embellished with these, forms immense 
rocks and vast elevations hanging over the sea, which, whenever they are broken to a certain 
depth, are found to contain these crystals, with capillary schorls, not very numerous. I have 
in my possession a group of needle-formed crystals from Mont St. Gothard, within which 
are seven small prisms of black striated schorl. The same may be observed in these minute 
crystals. One of these was perforated from side to side by a needle of schorl, the two ends 
of which projected out. The tormation of these capillary schorls must have preceded that 
of the quartzose crystals; otherwise it is impossible to conceive how the former should have 
penetrated the substance of the latter. In remelting the lava in a furnace, the quartz 
crystals remained perfectly unaltered.” 

Spallanzani also states, that in this lava are garnets and chrysolites more refractory in the 
fire than the matrix ; and he adds that since Dolomieu’s visit to the adjoining stoves, when 
the whole ground on which they stood was saturated with hot vapours issuing everywhere 
from small openings an inch or two in diameter, at the time of his own visit these were 
reduced to one, exhaling some sulphur and encrusted with soft pyrites. 


— 


iT RWS 


ON THE EFFECTS OF LONG-CONTINUED HEAT. 185 


mountain chains culminated to their utmost height. In the progress of re- 
frigeration the compressing and imprisoned forces became nearly balanced, 
and the residual predominance of the latter produces the phenomena of 
existing earthquakes and volcanoes. 

In the earlier periods, unmutilated skeletons, undisplaced scales, entire 
ink-bags, and florescent fronds, indicate conditions of nature which would 
now be called unnatural, a history of sudden death and speedy embalment, 
common, not to individuals only, but to generations and species. The pre- 
servation, in exquisite casts, of the most delicate organizations indicates a 
speedy but a tranquil entombment, which it would be difficult to refer 
to any other agency than that of gaseous emanation through the waters 
in which the plants and animals existed. Alcyonia and sponges, looking 
like recent specimens preserved in the places where they grew, point to a 
process of silicification, chiefly anhydrous, which anticipated decomposition. 
In the decreasing activity of internal heat and insalubrious emanations, we 
see the advancement of the physical and chemical conditions essential or 
advantageous to /ife; and with the progress of such conditions, favourable to 
the development of higher and higher forms of organization, we find a perfect 
correspondence in the natural history of organized fossils, and the increasing 
tones of the “ Diapason, closing full in Man.” 

From the theory of heat and the facts of geology, combined with physio- 
logical considerations, we learn that there was a definite era, in which the 
earth first became capable of supporting vegetable and animal life ; and we 
may account for the late appearance of man, by observing that there were no 
conditions adapted to the well-being and progress of human nature, till this 
state of things had yielded to a healthy atmosphere, a moderate heat, 
differentiated zones of life, stable forces, and a stationary standing ground. 

{In the rudimental ages of the earth we behold an ever-changing scene of 
new and fitful conditions passing in rapid succession. Through all the stages 
of its existence previous to the present uniformity, so favourable to the 
exercise of reason and the freedom of will and action, we see force gradually 
subsiding, and the time allowed to life expanded into a wider liberality. Our 
ideas of its duration, as compared with indefinite ages, are equally limited with 
our view of its magnitude, in comparison with space or matter ; we can find in 
geological data no chronology but that of priority; the fossil records even of 
its unconsolidated beds have not yet supplied us with the key of the cypher 
which should connect geology with human history. If ever we come to know 
the age of the primary rocks, or of the protozoic strata, it can only be by 
combining physical data with the experimental reproduction of granite, and 
a knowledge of the heat which the lowest organisms can bear, and live. 

Since Hall first applied chemistry to the service of geology, few attempts 
have been made in this country to pursue the path which he opened. In 
1833 the British Association entrusted to a commission, consisting of Prof. 
Sedgwick, Dr Daubeny, the late Dr. Turner,and myself, the task of illustrating 
geological phenomena by experiments which it was hoped might have thrown 
light on some of the subjects discussed in this Report. Disappointed of the 
greater part of the fruit of these experiments, I yet believe that the few 
results which I now lay on the table of the Section will not prove devoid of 
interest, especially as evidence of the low temperature at which bodies scarcely 
reputed volatile are capable of being sublimed. 

The iron furnaces of Yorkshire having been selected as furnishing the 
best field for these experiments, it fell to my lot to conduct them. Every 
facility was afforded me by the zeal and liberality of the proprietors and 
managers of two furnaces, one of which at Elsicar, belonging to the late Earl 
_ Fitzwilliam, and managed by Mr. H. Hartop, worked for a period of five 


186 REPORT—1860. 


years; the other at Low Moor, belonging to Messrs. Wickham and Hardy, pro- 
longed its unintermitting blast for fifteen years. The materials fur the experi- 
ments, in addition to those which I was myself able to supply, were provided 
partly by a grant from the Association, partly by an extensive donation of 
minerals and fossils from the stores of the Yorkshire Philosophical Society. 
Professor Phillips also, who was then in charge of that Society’s Museum, lent 
me his valuable assistance. 

The object kept in view, in devising experiments of so long a duration, was 
to subject the greatest possible variety of materials to the greatest possible 
variety of conditions, such as it might be presumed had formed, or altered, 
rocks, minerals, and mineralized organic remains. 

These were arranged in numerous crucibles, upright and inverted, and 
within two strong tripartite boxes of deal bound with iron thongs; one 
of these was stored with large blocks and copious powders of granite, basalt, 
limestone, grit, and shale, with whole and pounded minerals of every kind, 
hydrates and anhydrates, the ingredients of a great variety of minerals com- 
pounded in proper proportions, all the different salts and elements calculated 
to react upon them, with almost every metal adapted to form veins or to re- 
gister heat ; the other contained organic substances, fossil and recent plants, 
shells, corals, reptiles, and bones, disposed in clay, sand, chalk, marble, gypsum, 
fluor, sulphates, muriates and other salts of soda and potash which might dis- 
engage volatile elements by their mutual action, to react on fixed constituents. 

At the Elsicar furnace I was allowed, whilst it was being built, to insert 
crucibles in the back of the masonry in immediate contiguity with the body 
of melted iron. At Low Moor it was agreed to place boxes filled with cruci- 
bles and materials under the bottom stone, before the furnace was built. 
This stone, consisting of millstone grit, 15 inches thick, though it gradually 
wears hollow in the centre, retains the iron fused upon it usually for fourteen 
or fifteen years, without being materially impaired. In its crevices are often 
found the beautiful cubic crystals of nitrocyanide of titanium, first brought 
into notice by Dr. Buckland. 

In this situation the temperature to which the contents of the boxes would 
be exposed could not be exactly foreseen. It was presumed that in the centre 
it would be near to the melting-point of cast iron. It will be seen by refer- 
ence to Plates IV. and V., which give a section and plan of the furnace, that 
the boxes did not occupy the whole space beneath the bottom stone. It oc- 
curred to me therefore, when these had been placed in position on a bed of 
sand, covered with the same material, and built up with fire brick, to deposit 
round them in asimilar bed of sand, and enclose in like manner within walls 
of brick, lumps of various metals, and of granite, sandstone, fossiliferous 
shale, and limestone. From these supplementary experiments are derived 
the most interesting of the results which I have to describe. 

For when at the expiration of fifteen years the furnace was blown out, I 
found nothing left of the boxes but the iron straps with which they were 
bound, in a state of oxidation ; a few crucibles and portions of crucibles only 
had survived the general wreck of their contents ; granites, basalts, limestone, 
choice minerals, measured pieces, weighed powders and compositions, had 
disappeared ; all the exactness with which Professor Phillips had arranged for 
identifying the altered substances by their position and by comparison with 
reserved specimens, was lost labour. 

Nor did I find the deposits in the Elsicar furnace, at the end of five years, 
to have fared any better. From all these carefully devised experiments I can 
produce but two worthy of notice. One of them exhibits the conversion of 
river sand into sandstone, with a vacuity in its axis left by the volatilization 
of arecent plant, The stone has considerable tenacity, and came out of the 


. 
a 


a 


ON THE EFFECTS OF LONG-CONTINUED HEAT. 187 


erucible, with no adhesion to its sides, a perfect cast; no salt had been added 
to it, nor is any separable from it by boiling. The close cohesion of the 
grains of sand by the action of heat may have been facilitated by the inter- 
mixture of some impurities, referable to oxide of iron, and possibly to felspar. 
The only vestige of the plant is a skin of silica on the surface of the place 
which it occupied in the interior of the sand, coating the vacancy, but not 
furnishing an impression from which the character of the plant can be re- 
covered. ‘The stone showed signs of splitting from shrinkage in an oblique, 
or nearly vertical direction, a tendency which might probably have been more 
conspicuous had the experiment been on a larger scale. 

The other specimen is a translucent mineral of a pure blwe colour. This 
colour it does not lose when heated red-hot in the outer flame of a candle. 
Melted into a bead with carbonate of soda, it passes into a pure opake white ; 
the same also with a small proportion of borax; when the proportion of the 
borax is increased, the bead is transparent and colourless; dissolved in 
hydrochloric acid, the mineral loses its colour. The solution contains much 
sulphate of lime, and some silica and alumina, whether potash also, or soda, I 
have not determined ; tested with prussiate of potash, it shows no trace of 
copper; and none, or scarcely any, of iron. This substance therefore belongs 
to the class of minerals of which Lapis lazuli and Haiiyne are varieties. It has 
been formed irregularly under a thin crust of sand to which it adheres, is ini- 
bedded in sulphate, sulphide, and carbonate of lime, and accompanied with 
erystallized fluoride of lime. Whether this fluoride is a recomposition, or 
part only of the original mixture from which the blue mineral has been 
derived, I cannot say. The erucible certainly contained pounded fluor, and 
a sulphate, which underwent decomposition, and partially decomposed the 
fluoric crystals. 

But the objects to which I have alluded as possessing a new and unexpected 
interest, are the metals above mentioned as having been supplementarily 
placed, outside the boxes, under the bottom stone of the Low Moor furnace. 
The specimens consisted, originally, of pieces, of which chromographie plates 
have been appended to this Report, cut from a bar of zine, a block of tin, 
a pig of /ead, and a plate of tile-copper. They occupied, severally, the places 
marked in the accompanying ground plan of the furnace, 1, 2, 3, 4, as 
numbered at the time of the deposit. It will be seen that none of these 
pieces have undergone fusion, that of which the melting-point is lowest (the 
block tin) preserving perfectly its dimensions, the exact shape into which it 
was cut, and the sharp edges of the cutting. ‘The external coat of the 
tin, to the depth of from 1th to ith of an inch, is converted into deutoxide, 
crystalline, transparent, and of the same specific gravity as the native ore; 
between this and the metal, intervenes in some parts a space, which, with 
the striation of the metallic surface, indicates that a portion of the substance 
has been dissipated. 

Of the bar-zinc, more than half has been changed, though it preserves its 
original form, into a mass of crystalline oxide, interspersed with globules of 
the metal, burrowed in all directions with drusy cells and cavities, and 
showing extensive sublimation into the indurated sand which envelopes it. 
The nature of the sublimation is manifested by a number of prismatic spicula 
of metallic zine, about 4th of an inch long, standing within the cavities. 

But that which is chiefly remarkable is the tile-copper, in respect both to 
the temperature at which it has been volatilized, and the combination and 
interpenetration which its molecules, in a volatile state, have effected with its 
nearest neighbour, the dead. I have caused a drawing to be made of these 
specimens in their relative positions, as they lay in proximity to, but not 
touching, each other, having a portion of sand interposed. 


188 REPORT—1860. 


It will be seen that a very considerable portion of the copper plate has 
been dissipated, that the surface has been sweated down, and in some parts 
the whole substance has evaporated away. Bright crystals of red oxide of 
copper line the wasted surface, which is also covered above with a coat, 
ith of an inch thick, of mixed crystalline oxides of copper and lead; and 
in the hollow which the dissipation of the metal has left between it and the 
indurated sand, is a sublimate consisting of fine twisted coherent threads of 
metallic copper, like those met with in mines and slags. Where nearest to 
the lead, it has so intermixed its exhalations with those proceeding from 
that metal as to have spread over the upper leaden surface a coating of green 
crystals, consisting of a double oxide of copper and lead. Beneath, and round 
the lead, at its contact with the sand (which below has penetrated its sub- 
stance without altering its form), runs a pink skin, marking the path of the 
red oxide of copper. I cut the lump of lead in half, and found it not only 
traversed in the middle by a seam of mixed oxide, but, what was still more 
remarkable, dotted with spots of metallic copper, which had found their way 
to the very centre of the mass, and even reached the opposite side. 

That it was the metal in this case, as in that of the zinc, which became 
volatile, and was subsequently deposited in the form of specks and filaments 
of copper in some places, and combining with oxygen, as a crystallized oxide 
in others, cannot be doubted. To attribute these effects to thermal electricity 
would not be consistent with the facts; for there was here no contact, and no 
circuit. The penetration of the lead by the molecules of copper may be 
called Cementation, and be supposed to be due to capillary attraction of pores 
distended by heat acting on the volatile particles. 

But the surprising part of the result is, that the sublimation of copper by 
heat should have taken place at so low a temperature. These four metals, in 
close proximity, and all acted upon in the same manner, were their own 
mutual thermometers. It was impossible that the heat to which the copper 
plate, as a whole, had been subject could have been higher than the melting- 
point of the unfused lead and tin. I can attribute this unexpected fact to 
no other cause than the continual and protracted passage of hot currents of 
air and vapour, mingled perhaps with carbonaceous gas from the neigh- 
bouring wooden boxes*; and it seems probable that if the central portion 
of the bottom stone had withstood to the end the action of the furnace, or 
if the buried boxes had been protected with a vault of brick, more light 
might have been thrown on the transfer of molecules at moderate tempera- 
tures by similar effects produced on other materials. 

I owe an apology for having delayed this Report much longer than I 
should have done, had the bulk of the experiments been attended with better 
success. I have been reminded of them by the design of a member of the 
Association to institute some of a similar character with the added conditions 
of pressure and steam. Whoever should now undertake such experiments 
would conduct them on the vantage ground of the later researches which I 
have here noticed, and might obtain results of high interest to geological and 
chemical science. It may be doubted whether heat protracted through many 
years, or even extraordinary pressure, may be essential elements of such 
results. The unintermitted presence of volatile materials, for a considerable 
time, passing over and dwelling among those of greater fixity at temperatures 
mounting up to a red heat, may be the only needful condition; and if a fur- 


* Tf I am right in believing that an oolitic Echinus, Pecten, and Coral, and an Ammonite 
from the Lias, which I recovered from the furnace, are those marked in the Plan with the 
Nos. 8, 9, 10, then, as these were reduced to alkalinity, though without change of form or 
markings, it would follow that the carbonic acid under the same circumstances separates 
from lime at an equally low temperature of the mass, under the partial action of hot currents. 


ON THE EFFECTS OF LONG-CONTINUED HEAT. 189 


nace were appropriated to this object, it is not difficult to conceive a con- 
struction and application of it which would fulfil such a requirement. 

If any one could succeed in effecting the synthesis of pseuwdomorphic 
crystals, or of granites and porphyries, he would certainly perform a great 
service to chemical geology. In the first of these subjects of experiment 
success is scarcely to be looked for, except in the metamorphic action of 
heated volatile agents. It is possible that granite also, and porphyry, might 
be formed by a process of volatilization ; or they might perhaps be produced 
as a residual igneous crystallization out of a mass, of which the flux had been 
removed from the denser substances by sublimation, solution, or pressure. 

It should appear that the production of marble is also a problem still un- 
determined. Rose has expressed an opinion, founded on his own ex- 
periments, that the solid substance which Sir J. Hall obtained, by igniting 
chalk under a pressure that prevented the extrication of the carbonic gas, 
cannot have been marble. Possibly the presence of an excess of the acid 
may be an additional requisite to the production of a perfect specimen. 

Since this Report was drawn up, I have seen a memoir by M. Daubrée* 
which contains a very able and complete exposition of the progress of 
geological chemistry. His observations on the deposit of zeolitic crystals 
and other minerals discovered in the interstices of the old Roman brick- 
work and concrete at Plombiéres}, which have undergone the action of sili- 
cated waters springing from the earth at a temperature not, now at least, 
exceeding 158° F., seem to have solved the problem of the deposit of such 
erystals and minerals in the vesicles of basaltic rocks, and to have proved 
them to be due to aqueous infiltration whilst the rock was still hot. 

His views on the formation of another class of minerals, and the origin of 
the granitic and other early rocks, seem to be not equally satisfactory. To 
these he has been led by his own late experiments on the effect of aqueous 
vapour in decomposing obsidian and glass. He propounds, with the difftidence, 
however, which belongs to a hypothetical speculation, a theory to the 
following effect—that in a primeval state of the earth, when the heat now 
known to exist in its interior extended to the surface, as that surface cooled. 
down to a certain point, the red-hot obsidian, or silicated glass, of its first 
coat was decomposed by water condensed from a state of vapour, under 
great pressure, at a red heat; thus the quartziferous rocks were formed, at 
first as a plastic sponge, and when the water had evaporated as granite, the 
schist and slates immediately superincumbent upon it being the residuary 
product of the mother-waters. 

But this speculation is open to grave objections. What principle of 
solidification, it may be asked, capable of compacting graaite, is included 
in a process of disintegration? What has become of the silicates involved 
in it, to which we might look for such solidification, but whieh are absent 
from granite? The mother-waters which it supposes are incapable of dif- 
fusing the peculiar minerals encysted in the proximity of granitic rocks 
even to the distance of thousands of feet. No less unaccountable would be 
the absence of all the zeolitic and opaline substances that might have been 
expected. Everything tends to show that whatever the power of this process 
may be, it must be confined, at least, to the lavas, basalts, and trachytes. 

That heated water has been so universal a solvent as M. Daubrée supposes, 
is rendered very improbable by a circumstance noticed by Cagniard de 
Latour in his celebrated experiments on vapour highly heated and com- 

* Etudes et expériences synthétiques sur le métamorphisme et sur la formation des roches 
erystallines, 1860. 

T The presence of fluorine in the apophyllite of Plombiéres is remarkable, the more be- 


cause Vauquelin analysed the waters with the express object of detecting this constituent, 
and denied its supposed existence in them. 


190 REPORT—1860, 


pressed. In one of these, the addition of a crystal or two of chlorate of 
potash to water at the temperature of 648° F., proved sufficient to prevent 
any action of the aqueous vapour on the glass ; so easily was it saturated by 
the presence of a more soluble material. 

Neither is it at all probable that any stratum which can be supposed to have 
preceded granite under extraordinary conditions of heat and pressure, can 
have resembled in any degree obsidian or glass) M. Daubrée takes the 
vapour expansion of the ocean over the globe as equivalent to a pressure 
of 250 atmospheres, somewhat exceeding Mitscherlich’s supposition before 
quoted. On this pressure Mitscherlich, as has been said, sagaciously re- 
marked, that it would probably materially modify the chemical affinities 
of bodies, and prevent the formation of silicate of lime. His anticipation has 
been experimentally verified; and an equally remarkable instance of the 
same principle has been lately observed by Mr. Gore, who has found, on 
immersing some fifty substances in carbonic acid liquefied by pressure, that 
in that state it is chemically inert, to such a degree as not to dissolve oxygen 
salts. In these cases it should seem that pressure favours homogeneous, or 
simple, at the expense of heterogeneous, or complex, attractions ; and there is 
all the less reason for admitting M. Daubrée’s supposition, that obsidian, 
or any vitreous silicates, preceded the granitic rocks. 

We may carry these ideas further ; we may extend our speculations from 
the heat and weight of a vaporized sea to the gaseous system of Laplace, and 
the ultimate atoms of Newton. ‘Then, as the heat by degrees radiated into 
space, and as the repulsive force yielded to the forces of attraction, the 
first compounds would be of the simplest order,—water, and hydrochloric 
acid,—the chlorides of potassium, sodium, silicon, and aluminium, the oxides 
of magnesium and calcium, with others of a like class. Here we have both 
the materials of the sea, and of the primary crust of the earth; and at the 
same time all the power of consolidation which free crystalline force and 
enormous pressure can give to materials indisposed by that pressure to enter 
into complicated combination. 

In contemplating the origin of granite, it is not, however, competent to 
us to regard it as a fundamental rock only, since it preserves the same 
erystalline character under various conditions of heat and pressure. But 
we must remember that the gaseous theory which we are imagining implies 
a residue, in an internal gasometer, of similar primary compounds confined 
in a highly heated, condensed, and elastic state at no great distance under 
our feet, from the sudden or gradual evolution of which it is not difficult 
to conceive that all the eruptive rocks and veins, and many of the pheno- 
mena of consolidation in the sedimentary strata, may be accounted for. 

Every rock of eruption, and every mineral vein, which has shot up into the 
strata, indicates such an origin. The porphyries, trachytes, basalts, and lavas 
are essentially chemical and erystalline compounds. They differ from the quart- 
ziferous rocks only in this, that the chief part of the siliceous ingredients which 
characterize the latter having been antecedently used up, the greater fusi- 
bility of the former has more or less obliterated their crystalline structure. 

In these speculations it matters not from what source we suppose the 
heat of the earth to have been derived. Perhaps, a law of gravity, together 
with the other forces of attraction, imposed on the ultimate particles of 
matter, may account for all the heat which is, or has been inthe world. In 
any case, the most probable inductive conclusion from our knowledge of 
the earth’s heat, and the phenomena of eruption, with the light thrown on 
the production of minerals by Daubrée’s first sertes of experiments, and 
those of Durocher, appears to be, that mineral veins and eruptive rocks 
are the result of gaseous combinations and reactions. As regards mineral 


—— 


43> 


ee oe ee ee ee ee 


> De a eran nei 


ON THE EFFECTS OF LONG-CONTINUED HEAT. 191 


veins, this, I believe, is the opinion of most observers. But we see the same 
metamorphic effects which are produced by them, equally produced by the 
presence of any eruptive rock. If a stratum of limestone be invaded, and a 
portion of it included in the invading substance, that portion is not unfre- 
quently impregnated with magnesia and converted into dolomite, equally by 
a mineral vein or a granitic rock. 

The advantages which this theory possesses over any that have yet pre- 
sented themselves, are that it accounts for all the following phenomena :— 

1. The characteristic structures of granite, and of gneiss and mica-slate,— 
which may be compared to the deposits of graphite in gas-retorts, solid 
where the carburetted gas aggregates its decomposed molecules of carbon in 
confinement, but faliated and quasi-stratified, where the gas chances to escape 
through cracks in the retort into the more open chamber of brick-work ;— 

2. The perfect uniformity of crystalline texture in granite, whether deep or 
superficial, in thin veins or solid masses, showing that neither great pressure 
nor slow cooliug have been essential conditions of its crystallization ;— 

3. The wide diffusion of zones or atmospheres round the eruptive, and 
especially the granitic rocks, of mineral substances, and metamorphic effects, 
a phenomenon which, together with that of the filling up of mineral veins 
from below, is not accounted for by any other theory ;— 

4. The metalliferous and quartziferous impregnations of the sedimentary 
strata. 

If, with Cordier, we divide the eruptive rocks into the guartzose (which 
correspond to the granites and earliest porphyries) ; and the wnquartzose, 
comprehending the fe/spathic (which correspond to the later porphyries and 
trachytes) ; with the pyroxenic (which correspond to the basalts and lavas) ; 
and if we consider all these as originating from gases, accompanied by 
aqueous vapour,—then the phenomena show the amount of such vapour 
present in the guartzose formations to have been almost infinitesimal, 
whilst that which attended some parts of the pyrowxenic formations was con- 
siderable. As regards the sedimentary siliciterous rocks, they show, in the 
semiopaline, semiquartzose composition of the siliceous beds, the action of 
anhydrous gas, aided by aqueous vapour. Aqueous vapour acts on silicates 
only at a heat approaching redness, and conveys no silica. Chloride of silicon 
would carry silica, and would diffuse it at a much lower heat, since it boils 
at a temperature below 140° F. 

Connected with the preceding speculations the following remarks may 
deserve attention. There is a singular resemblance of mineral and erystal- 
line constitution between the pyrozenic rocks and meteoric stones,—a re- 
semblance, in fact, so close as to indicate a similar mode of production out 
of the same materials. The late optico-chemical discoveries of Bunsen and 
Kirchhoff have shown, with a great degree of probability, that molecules of 
tron, nickel, and magnesium abound in the solar atmosphere; should the 
progress of those discoveries add silicon to this list, we have here again the 
chief materials, both of meteorolites and of pyroxenic rocks. In any ease, 
whether we suppose the meteorite to have been contemporaneous with the 
earth, or to be ejected from the moon, or emitted from the sun, our thoughts 
are led back to a time when the whole solar system consisted of the same 
ultimate atoms, and are confirmed in the opinion that the meteorites and the 
fundamental rocks of the earth have undergone similar processes of mole- 
cular and erystalline combination, the vitreous coat of the meteorite, and the 
vitreous character of the later lavas, being due also to the same causes :— 
Ist, to the fusibility of the material; 2ndly, toa more intense heat generated 
by a nearer proximity to an oxidating atmosphere; 3rdly, to a more rapid 
rate of cvoling. 


192 REPORT—1860. 


What our views, however, of the original constitution of matter may be, 
is a point of less consequence than what are the conclusions in geology to 
which we are conducted by observation and experiment. The general con- 
clusions to be drawn from the foregoing researches seem to be these :— 
That no theory of the earth consists with the phenomena, which does not 
take into account a heat of the surface once amounting to redness ;—that 
the most prominent chemical and crystalline compounds which laid the base- 
ment of the earth’s crust, and continued to penetrate it, as far as into the 
tertiary strata, have disappeared in the present eruptive system ;—that the 
nature, force, and progress of the past conditions of the earth cannot be 
measured by its existing conditions ;—that to deduce accurate inferences in 
the sciences of observation, the attention requires to be directed less to gene- 
ral analogies than to specific and essential distinctions. 


EXPLANATION OF PLATES. 
PLATES IV. & V. 


Section, and Plan, of the furnace in which the deposits lay for 15 years, the number 
of each deposit, external to the boxes, being marked on the plan. 


PLATE VI. 


Fig. 1 (Plan No.4). Tile copper 5 in. X 2} in. X 3 in, coated with laminz of dark, 
red, crystallized oxide of copper, alternating with white and yellow crystallized prot- 
oxide of lead, and with a pink intermixture of crystallized oxides of copper and lead 
covered with sand indurated, but not vitrified, by protoxide of lead. 

a. Twisted filaments of metallic copper. 6. Crystals of red oxide. 

bb. Lamine of crystallized red oxide of copper alternating with protoxide of 
lead, and mixture of oxides of lead and copper. 

c. Particles of metallic copper. ec. Golden metalline spot. 

Fig. 2 (Plan No. 3). Pig lead, 4} in. x 3} in. X 2} in, View of upper surface, show- 
ing green and yellow double oxides of lead and copper, with spots of metallic copper. 

d. Cavity from which lead has sublimed. 
e. Spots of metallic copper. 
f. Double oxides of lead and copper. 


PLATE VII. 

Fig. 3 (Plan No. 3). Pig lead, vertical section, showing exterior and interior 
seams of mixed oxides of lead and copper, green, yellow, and red, with spots of me- 
tallic copper. 

g. Red oxide of copper between lead and indurated sand. 
h. Spots of metallic copper in the interior of the lead. 
i. Oxide of copper and lead. kk, Lead hardened by disseminated oxide. 

Fig. 4 (Plan No.4). Enlarged section of part of fig. 1, showing threads of metallic 
copper. 

Nie. 5 (Plan No.4). Part of fig. 1; enlarged view of pink mixture of crystallized 
oxides of copper and lead, with spots and threads of metallic copper. 


PLATE VIII. 


Fig. 6 (Plan No, 2), Block tin, 3 in. X 2 in. X 1 in., with a coat of transparent cry- 
stallized deutoxide from } in. to 4inch thick, 
1. Striated surface of metal beneath oxide. 
m. Crystals of deutoxide, transparent and colourless. : 
Fig. 7 (Plan No. 1). Zine bar, in indurated sand, fractured, showing a surface 
partly metallic, partly crystalline. 
n. Spiculz of sublimed metal. o. Seam of metal. 
Fig. 8 (Plan No.1). Showing cavernous face of oxide of zinc with crystals of do. 
p. Cupped hollows set with crystals of oxide of zinc, out of which globules of 
metal have sublimed. 


Bottem Stone 16 inches thack 


Dara Tar i ie TO 7 


aq7ia wae en a ores | 


D ‘ 


a od s nt th 
ara yin Me, 


REFERENCES. 


cies Iron rests upon the bottom Stone in the space < feet 4inches in the Section 
and the blast 1s introduced at the small Grclein D° The rigures tronv 1 te 23 on 
the Ground Plan represent the order and situation of the Deposits made in the cavity 
“on the outside of the Boxes. Lhe black tines in the centre of the Ground Plan repre - 
"sent the two Boxes whose two sides meet exactly tn the centre of the Furnace. 

e letters GR.B.C.D, agree with those marked on the Bocces. 


N° L. Zine bar. 2. Coral tn Coral Rag, Tie how Moor Pig Trow. 
; 2 Block Tin. ih = Jo. Lecten in Malton Oolite. 18. Septarium. 
" 4 3. Lig lead. plates Al. Coral, recent . 19. Flagstone : 
4. Tile Copper.| -7-8. LR. halk, 20. Granite . 
5. Lit Shale trom Black Ironstone. 13. N° 11,395. 2L. dnamonite trv Lias . 
6. Black Ball Zronstone. 4. Whale Vertebrx. 2%. Basalt. 
7. Jet. Ls Blue linestone with Shells, 23. Granite Yorks Streets 


8. Echirats in Malton Ovlite. 16. Magnesian Lanesterve . 


ia 
l 
f 


Ground Plan of the furnace . 


Opening where the Blast is introduced 


Bottom Stone L6 tnehes thick. 


Ts 


Front Arch where the 
Furnace ts worked. 


ae ra 

Ss Pe Fas 

2. ee ae 
+e at » 
oe 


> . + 
Oe tes : 
» 2 Aw wick j ba 3° “ae. 
Bf Foe es * 
; Cr ee “ 
7" RIOTS om 
* "y 2 e Pas © 


(Plan V°4 : 


(Plan V?3.) 


Fig 4& 
Plan Ni 4) 


hig 3 
(Plan 


Fig. 7. 
(Plan N71) 


fig. 6. 
(Plan ¥* 2) 


Fig. 8. 
(Plan N’1) 


ON STEAM-SHIP PERFORMANCE. 193 


Second Report of the Committee on Steam-ship Performance. 


CONTENTS, 

Report. ’ 

Appendix No. I.—Table 1. Table showing the results of performances at sea and on 
the measured mile, of 17 vessels of the Royal Navy, of 22 vessels in the Merchant 
Service, and of two vessels of the United States Navy, together with the particulars 
of their machinery. 

Table 2. Return of the results of performances of 49 vessels in the service of the 
Messageries Impériales of France during the year 1858. 

Appendix No. II.—Table 1. Quarterly returns of the speed and consumption of coal 
of the London and North-Western Company’s express and cargo boats, under 
regulated conditions of time, pressure, and expansion; from January 1 to De- 

cember 31, 1859. 

Table 2. Half-yearly verifications of consumption of coal of the above vessels, 
from January 1 to December 31, 1859. 

Appendix No. ITI.—No. 1. Form of Log-book used by the Royal Mail Company. 

No. 2. Form of Log-book used by the Pacific Steam Navigation Company. 

No. 3. Form of Engineer’s log used by the Peninsular and Oriental Company, 

No. 4. The Admiralty Form for recording the trial performances of Her Majesty's 
steam-vessels. 

No. 5. Board of Trade Form of Surveyor’s Return of Capabilities. 

Appendix No. IV.—Table 1. Showing the ratio between the indicated horse-power 
and the grate, the tube, the other heating, and total heating surfaces; also, between 
the grate and heating surfaces, and between the indicated horse-power and the coal 
consumed, 

Appendix No. V. Letter from Mr. Archbold, Engineer-in-Chief, United States Navy. 
Description of the hull, engines, and boilers of the United States Steam Sloop 

‘Wyoming’. 

Table 1. Return of performance of the ‘ Wyoming’ under steam alone. 

Table 2. Return of performance of the ‘Wyoming’ under steam and sail combined. 
Table showing the trial performances of the steam-vessels ‘Lima’ and ‘ Bogota’ 

when fitted with single cylinder engines, and after being refitted with double 

cylinder engines. Also the sea performances of the same vessels under both these 

conditions of machinery and on the same sea service. 


Report. 


Ar the Meeting of the British Association, held in Aberdeen in September, 
1859, this Committee was re-appointed in these terms :— 

“That the following Members be requested to act as a Committee to con- 
tinue the inquiry into the performance of steam-yessels, to embody the facts 
in the form now reported to the Association, and to report proceedings to 
the next meeting. 

“That the attention of the Committee be also directed to the obtaining of 
information respecting the performance of vessels under sail, with a view to 
comparing the results of the two powers of wind and steam, in order to their 
most effective and economical combination. 

“That the sum of £150 be placed at the disposal of the Committee for 
these purposes.” 

The following gentlemen were nominated to serve on the Committee :— 


Vice-Admiral Moorsom. William Smith, C.E. 

The Marquis of Stafford, M.P. J. E. M¢Connell, C.E. 
The Earl of Caithness. Charles Atherton, C.E. 
The Lord Dufferin. Professor Rankine, LL.D. 
William Fairbairn, F.R.S. J. R. Napier, C.E. 

J. Seott Russell, F.R.S. Richard Roberts, C.E. 
Admiral Paris, C.B. Henry Wright, Hon. See. 


The Hon. Capt. Egerton, R.N. 
1860. o 


194 REFORT—1860. 


Your Committee, having re-elected Admiral Moorsom to be their Chair- 
man, beg leave to present the following Report :— 

They have held monthly meetings, with intermediate meetings of sub- 
Committees appointed to carry out in detail matters referred to them by the 
General Committee. The Committee regret that they were deprived of the 
services of one of their members, Mr. Charles Atherton, at an early stage of 
the present inquiry, his public duties preventing his attending. 

They have been assisted by Corresponding Members ; noblemen and gentle- 
men, who, not being members of your Association, were not, by its rules, 
eligible as members of your Committee. Some of them, however, being 
owners of steam yachts, and others intimately acquainted with all matters 
relating to steam shipping, their cooperation was considered very essential, 
as introducing to the Committee gentlemen, not only capable of dealing with 
the subjects of this inquiry, but who also had it in their power to place in 
the hands of the Committee, materials, which, it is confidently hoped, will 
eventually lead to a correct and scientific knowledge of the laws governing 
economic Steam-Ship Performance. 

The Corresponding Members so elected were :— 


Lord Clarence Paget, M.P., C.B., &e. | Capt. William Moorsom, R.N. (since 


Lord Alfred Paget, M.P. deceased). 

Lord John Hay, M.P. Mr. John Elder. 

The Hon. L. Agar Ellis, M.P. Mr. David Rowan. 
The Earl of Gifford, M.P. Mr. J. E. Churchward. 


The Marquis of Hartington, M.P. Mr. Thomas Steele. 
Viscount Hill. 


It will be within the recollection of the Association that the labours of this 
Committee last year were almost exclusively devoted to explaining to the 
various shipping companies and others with whom they were in correspond- 
ence, the objects proposed, and suggesting such forms as, if accurately filled 
in, would accomplish the purposes contemplated by the British Association. 
Log-books were prepared, and copies furnished to the leading Steam Packet 
Companies. 

At their first meeting the Committee took into consideration the manner 
in which the grant of money placed at their disposal by the Association could 
be most judiciously applied, and after mature consideration it was unani- 
mously resolved :— 

“That to procure information from shipbuilders and engineers, it is found 
to be indispensable to hold personal intercourse with them, without which 
little progress is likely to be made.” 

The Honorary Secretary was accordingly deputed to wait upon the prin- 
cipal Shipbuilders, Engineers, and Steam Shipping Companies in London 
and its vicinity, to explain the objects of the Committee, and to solicit their 
cooperation by furnishing the Committee with authenticated returns of the 
sea performances of vessels, as well as of their trial trips. 

In this your Committee are happy to report that they have succeeded. All 
to whom application was made expressed concurrence in the objects of your 
Committee, and their willingness to render every information in their power. 
The great difficulty was to make a suitable selection of vessels as examples 
of ordinary performance in the mercantile navy. Press of business, and 
perhaps want of thoroughly understanding the aims of the Committee, induced 
them to throw the whole labour of making these returns upon the Committee. 
The log-books for a number of years, and any documents the Committee 
desired to see, were freely placed at their service; but the time required to 


ON STEAM-SHIP PERFORMANCE. 195 


wade through the masses of logs, together with the fact of the Association 
_ meeting this year nearly three months earlier than usual, rendered it imprac- 
_ ticable for more than a limited amount of work to be got through. It was 
therefore determined to make a selection of certain vessels, and to endeavour, 
as far as possible, to render complete the record of a few. 

Your Committee at the same time communicated with the Admiralty, with 
a view of instituting a similar comparison between the trial trips and ordinary 
performances of Her Majesty's vessels at sea. 

They much regret that they have not been able to obtain the latter. The 
Lords Commissioners, however, very courteously entrusted the Committee 
with the original returns of Her Majesty’s vessels during the years 1857, 
1858, and 1859, as furnished by the officers who conducted such trials, with 
permission to copy and make any use they thought fit of the information 
they contained. Diagrams of the engines taken on the trials during the year 
1859 were also furnished. ' 

Your Committee must remark with regard to these trial performances, that 
they do not appear to be instituted with any other view than as a trial of the 
working of the engines, excepting in a few instances, when experiments have 
been made to test the merits of certain screws. In very numerous cases, the 
officer distinctly reports that the boiler power is insufficient. The speed 
may or may not be taken at the convenience of the officers, but in no case 
: : any note taken of the economical efficiency of the engines with regard to 

uel. 

As your Committee are restricted to a record of facts, it is out of place 
__ here to suggest changes in the mode of conducting the trials of Her Majesty’s 
_ ships. The Committee would, however, fail in their duty if they did not avail 
themselves of this occasion to repeat their conviction, as expressed in their 
last Report,—“ That it would tend to the advancement of science, the im- 
provement of both vessels and engines, and to the great advantage of Her 
Majesty’s service, if the trials of the Queen’s ships were conducted ona more 
comprehensive plan, directed to definite objects of practical utility on a 
scientific basis, and recorded in a uniform manner.” 

In addition to the vessels of the British Royal and Mercantile Navies, your 
Committee have great pleasure in being enabled to lay before the British 
Association a return of forty-nine vessels in the service of the Messageries 
_ Impériales of France, obligingly furnished by a member of the Committee, 
Admiral Paris, and recorded in the form used by that Company ; also, of 
__ two vessels belonging to the United States Navy, the particulars of which 

have been extracted from the second volume of Mr. Isherwood’s recent 
__ publication, entitled “ Engineering Precedents.” They have been introduced 
_ into the Tables (see Appendix, Table I.). 

While this Report was preparing, the Committee were gratified by receiv- 
ing from Mr. Archbold, Engineer-in-Chief, United States Navy, two sets of 
tabulated returns of performance of the United States steam sloop of war 
_* Wyoming,’ under steam alone, and under steam and sail. 

___These returns are of peculiar value, as comprising particulars in a form 
which the Committee believe has never yet been published. Along with the 
_ data afforded by Mr. Isherwood’s book, they give the area of sail spread and 
_ the force of wind by notation, together with other particulars, useful for 
_ caleulations of results and for comparisons. 
_ These Tables are contained in the Appendix, with Mr. Archbold’s letter, 
and a description of the hull, engines, and boilers of the ‘ Wyoming.’ 
The returns furnished by the British Admiralty embrace 216 vessels and 
_ $53 trials, with about 900 diagrams. For the same reason as above stated, in 
o2 


— ere CU 


————————— 


‘© 


os ee agen fd Pe 


paneer 


Or ot ales) 


a 


196 REPORT—1860. 


case of merchant vessels your Committee were obliged to make a selection, 
and to endeavour, for the purposes of the present Report, to obtain a complete 
record of a few, in the form suggested by the Committee. With this view, 
application was again made to the Admiralty, asking for the additional parti- 
culars not embraced in the returns of trial performances already furnished, 
and stating that their Lordships were, of course, aware that the particulars 
given in those documents were of comparatively small value without others 
of the vessels, their engines, screws, and boilers. The Committee added 
that they were in possession of such full particulars from both companies and 
private firms, and they trusted also to be favoured with similar information 
from the Admiralty. To this communication, the Lords Commissioners re- 
plied that they regretted they could not at present supply the information 
desired; but they would be glad to receive a copy of the reports obtained 
from companies and private firms. Your Committee thereupon constructed a 
Table embracing the particulars of merchant vessels (Appendix I., Table 1), 
and also a blank table filled in with the names of Her Majesty’s vessels, 
selected as before mentioned, and containing the results of the test trials 
already given, and furwarded them to the Admiralty, begging that they 
might be favoured with the return of the table of the ships of war with the 
blanks filled in, adding, that if pressure of public business should prevent 
that being done, your Committee would send a person to copy the particulars 
on receiving the sanction of the Lords Commissioners to such a course. 

As a measure of precaution in case of failure on the part of the Admiralty 
to send the promised particulars in time for printing, your Committee ob- 
tained returns of the machinery of these vessels by application to the manu- 
facturers, personally and by letter. They avail themselves of this opportunity 
to thank Messrs. Boulton and Watt, Maudslay Sons and Field, and John 
Penn and Sons, for having so fully and so promptly responded to the call. 
They are, therefore, now enabled to lay before the Association a table com- 
prising the results of the trials furnished by the Admiralty, together with the 
particulars of engines, &c., furnished by the manufacturers: the figures in 
Clarendon type (see Appendix I. Table 1) denote the Admiralty returns, 

Your Committee regret that there are some particulars of the trials still 
wanting, as, for example, the evaporation of water and the consumption of 
fuel; but they believe that hitherto those items have not been recorded, It 
is earnestly hoped, now that public attention has been called to the subject, 
that a more exact and careful account may be taken, both on the measured 
mile and on ordinary service at sea. 

In compiling the Table of merchant vessels, a similar course has been 
adopted, viz. of gathering from the best sources the various details necessary 
to complete the Table. The Companies to which the vessels belonged, gave 
every information in their possession, not only of the vessels themselves, but 
also of their actual sea performances, and placed at the disposal of the Com- 
mittee the sea logs for every voyage, with permission to make such extracts 
as they deemed proper. For any additional information, they were referred 
to the constructors of the engines and vessels. Your Committee cannot 
speak in too high terms of the constant readiness to give information, 
although at considerable inconvenience to themselves, which the various 
Companies and private firms have invariably shown. They feel assured that, 
had time permitted, and if the requisite labour could be devoted to it, the 
whole shipping community would willingly contribute their quota of statistics : 
all that is wanted is uniformity of arrangement, and that a form similar to the 
one proposed by the Committee be generally adopted. 

The thanks of the British Association are especially due to the Royal 


ON STEAM-SHIP PERFORMANCE, 197 


Mail Steam Packet Company, to the Pacific Steam Navigation Company, to 
the London and North-Western Railway Company, to Messrs. Inglis Bro- 
thers, Messrs. Randolph and Elder, Messrs. Caird and Co., Messrs. R. Na- 
pier and Sons, and to Captain Walker, of the Board of Trade. 

Captain Walker very obligingly placed at the service of the Committee 
some of the books in which the vessels registered and surveyed by the Board 
of Trade are recorded, and your Committee are in possession of copies of the 
entries of 51 vessels, varying from 600 to 2000 tons register and upwards, 
registered in the ports of London, Liverpool, Southampton, and Glasgow, 
during 1858. These have formed a very useful guide in leading to a selec- 
tion of vessels from which to obtain the particulars requisite for comparison. 

Your Committee have been in communication also with the French and 
American ambassadors, with a view to obtaining the statistics of perform- 
ance of their respective navies ; and, after referring the matter to their home 
Governments, the Committee have received the assurance of their willingness 
to cooperate. 

Your Committee, being precluded by the terms of their appointment from 
discussing theories, or attempting to deduce laws, have, nevertheless, thought 
it not inconsistent to prepare a table of ratios based on the indicated horse- 
power, and showing the ratio between that element, as developed on the 
measured mile, and the grate, the tube, and other heating surfaces of the 
boilers producing it; also, between the grate and heating surfaces, and be- 
tween the indicated horse-power and the coal consumed. The Committee 
regret that this important item, the coal, is not more frequently recorded, 
very few private trials making any note of it; and in no instance brought 
under the notice of the Committee, have the Admiralty officers made known 
this element, so necessary for ascertaining the efficiency of the boilers (for 
Table of Ratios, see Appendix IV. Table 1). 

The following is a general summary of the result of the Committce's 
labours during the past session. They have obtained :— 

1. Returns of 353 trials by 216 of Her Majesty’s vessels of war during the 
years 1857, 1858, and 1859, with about 900 (898) diagrams taken during 
the trials in 1859; also notes, by the officers conducting the trials, of 
observed facts. 

Of these trials, fifty-eight made by seventeen of the vessels, have been 
selected by way of illustration, with the particulars of machinery obtained from 
the makers, and arranged in a tabular form. (See Table 1, Appendix 1) 
The names of the vessels are the ‘ Diadem,’ ‘ Doris,’ ‘ Mersey,’ ‘ Marlborough,’ 
‘Orlando,’ ‘Renown,’ ‘ Algerine,’ ‘Bullfinch,’ ‘Centaur,’ « Flying Fish,’ 
‘ Hydra,’ ‘Industry,’ ‘ James Watt,’ « Leven,’ ‘ Lee,’ « Slaney,’ and ‘ Virago.’ 
This Table also comprises the two American vessels, ‘ Niagara’ and ‘ Massa- 
chusetts,’ together with the British vessel ‘ Rattler,’ introduced for compari- 
son. 

2. Returns of 68 merchant vessels. 

Four diagrams taken during trials of the ‘ Atrato.’ 

Scale of displacement of the ‘ Atrato.’ 

Lines of ditto. 

Eight diagrams of the ‘Shannon’ taken during trials. 

Twenty-two of these vessels have been selected and tabulated. (See Ap- 
pendix I. Table 1.) Their names are— Anglia,’ ‘Cambria,’ ¢ Scotia,’ ¢ Tele- 
graph,’ ‘ Mersey,’ ‘ Paramatta,’ ‘Shannon,’ ‘ Tasmanian,’ ‘ Oneida,’ ¢ Atrato,’ 
‘La Plata,’ ‘Lima,’ ‘San Carlos,’ ‘ Valparaiso,’ ‘ Bogota,’ ‘ Callao,’ Guaya- 
quil,’ ‘ Undine,’ ‘ Erminia,’ ‘ Admiral,’ ‘ Emerald,’ and ‘John Penn. 

The returns of the first four, belonging to the London and North-Western 


198 REPORT—1860. 


Railway Company, are the mean of a number of trips on actual service be- 
tween Holyhead and Kingstown. ‘The returns of the ‘ Erminia,’ ‘Admiral,’ 
‘Emerald,’ and ‘John Penn,’ are measured mile performances only ; but the 
remaining 12 vessels, with the exception of the ‘ Undine, show their sea 
performances over distances of about 6000 consecutive nautical miles each, 
in addition to the performances on the measured mile. 

3. Return of the results of performance of 49 vessels in the service of the 
Messageries Impériales of France, recorded in the form used by that Com- 
pany. ‘The whole of these vessels are given in the Appendix. (Appendix I. 
Table 2.) 

4. Quarterly returns of the speed and consumption of coal of the London 
and North-Western Company’s express and cargo boats, under regulated con- 
ditions of time, pressure, and expansion, from January 1st to December 31st, 
1859—presented by Admiral Moorsom. (Appendix II. Table 1.) 

Half-yearly verifications of the consumption of coal of the above vessels, 
from January 1st to December 31st, 1859, (Appendix II. Table 2.) 

5. Forms of log-book used by the Royal Mail Company (Appendix III. 
No. 1), by the Pacific Steam Navigation Company (No.2), by the Peninsular 
and Oriental Mail Company (No.3), the Admiralty form for recording trials 
of Her Majesty’s vessels (No. 4), and the Board of Trade form of return of 
capabilities (No. 5). 

6. Table showing the ratio between the indicated horse-power and the 
grate, the tube, the other heating and total heating surfaces; also, between 
the grate and heating surfaces, and between the indicated horse-power and 
coal consumed. (Appendix IV.) 

From the above list, it will be readily conceived that the time of the Com- 
mittee has been fully occupied, as the task of copying and condensing from 
log-books is one involving a large amount of labour. Your Committee have 
not therefore, as yet, been enabled to conduct experiments on the plan 
recommended in their first Report presented to the Association in Aberdeen. 
They have, however, kept that branch of their inquiry in view; and through 
the courtesy of Mr. A. P. How, of Mark Lane, and of Messrs. Tylor and 
Sons, of Warwick Lane, they have been presented with apparatus of the 
value of about £60, consisting of salinometers, and an engine counter and 
clock; they have also at their disposal, for use whenever required, a superior 
dynamometer, and a compound stop-watch, and are now prepared to pro- 
ceed with experiments, should the Association see fit to renew their powers, 
and the consent of the Government be obtained. 

The Committee regret that they have not been able to collect any such 
information respecting the performance, under sail alone, of steam-vessels, 
as was contemplated by the Association, “with a view to comparing the 
results of the two powers of wind and steam, in order to their most effective 
and economical combination.” 

They must, however, draw attention to the synopsis given by Mr, Isher- 
wood, of the steam-log of the ‘ Niagara, in which her performances, “ under 
steam alone,” “under steam and fore-and-aft sails,” and “‘ under steam and 
square sails combined,” are set forth in such manner that those conversant 
with the subject will be enabled, without much difficulty, to assign its approxi- 
mate value to the power of the sails alone. 

In Mr. Archbold’s Table of the performance of the ‘ Wyoming,’ the addi- 
tional particulars of the force of the wind by notation, the area of sail set, 
and the indicated horse-power, which are not always stated in Mr. Isher- 
wood’s synopsis, afford the means of tolerably accurate comparison. 

It is a duty the Committee owe to themselves, to express thus publicly 


ON STEAM-SHIP PERFORMANCE. 199 


their sense of the services rendered to the Association by Mr. Henry Wright, 
their Honorary Secretary, whose untiring energy, indefatigable labours, judg- 
ment, and discretion, have enabled them to lay this information before the 
meeting. 

To Mr. Smith, a member of the Committee, their acknowledgements are 
due, as well for the use of a room in his offices, as for several sources of 
information opened to them by his influence. 

The Marquis of Stafford, by placing a room in his house at the disposal 
of the Committee for occasional meetings, has contributed materially to the 
personal convenience of the members. 

Of the grant of £150 voted by the Council of the Association, to defray 
the expenses of printing, postage, collecting information, &c., £124 3s. 10d. 
has been expended, viz.— 


o's fe 

Peprniuog last year’s Report ....... ...0--00cesncces Beware) oot 
SenmrIMinn present Report. ... 52). -saa- sees ecco recess (8 14.0 
To stationery and miscellaneous printing = GU Gt Mieedeecltn..0 5) RG Dee D 
EMUMINEIE sic ne, 2 50S iv Mete sae amo satel v olple ey ia bide She whee a ‘iain abe 
To sundry expenses, ‘including cab hire and railway fares, incurred 812 6 
by the Honorary Secretary whilst collecting information .... 812 6 
Votal expenditure 55.5% Vit. Fae. he's £124 3 10 


Balance of grant remaining unexpended....£25 16 2 


It was originally intended to institute inquiries, not only in London and its 
vicinity, but also in Glasgow, Liverpool, Hull, Bristol, Southampton, New- 
eastle-on-Tyne, &c., and for this purpose it would have been necessary to 
defray the expenses of an agent to conduct the inquiry; but the shortness 
of the session, together with the extended field which London presents, ren- 
dered that course impracticable. 

Your Committee feel, that a beginning having thus been made towards the 
means of a scientific investigation of the performance of ships under differ- 
ing conditions at sea and in smooth water, it would ill become the British 
Association for the Advancement of Science to drop the question, although 
expense as well as trouble is involved in its successful pursuit. 

They recommend the reappointment of a Committee, with a renewal of 
the grant, and with power to remunerate a clerk for such services as cannot 
be undertaken by any of its members. 

On behalf of the Committee, 
C. R. Moorsom, Vice-Admiral, 


19 Salisbury Street, Strand, London, Chairman. 
June 13th, 1860. 


WNote.—Since the above Report was written, and whilst in the press, infor- 
mation was forwarded to the Committee which has enabled them to compile the 
Table given in the Supplementary Appendix, showing very interesting com- 
parative results of two vessels, the ‘Lima’ and ‘ Bogota,’ when fitted with 
different systems of machinery. The Table shows the results of perform- 
ances on trial of these vessels when fitted with single-cylinder engines, and 
also at sea on a voyage of upwards of 6000 miles; also their performances 
when fitted with double-cylinder engines. 


ERRATA.—Larce TABLE—APPENDIX I. 


‘ Atrato’ on trial, Stokes Bay, Jan. 22, 1857, omit Indicated Horse power 1128°42. 
Ditto, ditto, Mar. 4, 1857, for Indicated Horse power 1198°22° 
yead 2396°44, 


200 


Appenp1x I.—TAsBLE 


Name of vessel. 


Guirinal ........... 


Seer +2 ane 
Méandre 


eee eeweneeee 


sere eeeee 


QOBITIS 5 i052 ateuien oat 


Bosphore ........- 
Hellespont ........ 
Qronteecsssed.<.2 
Philippe Auguste 
Merovée 
Cheliff 


Aventin ..........+. 
Leonidas ..........+ 
Tage ¥ 
Tancréde 

Télémaque 
Amsterdam 
Périclés 


se eeereeeee 


Totals 


see eeeene 


Nominal horse-power. 


REPORT—1860. 


2. 


revolutions. 
Mean number of reyolu- 
tions by counter. 


Corresponding number of 


| 24 
| 27-5] 2 


h num- 


Nominal power realized 
ber of revolutions obtained. 


corresponding wit 


Total distance run. 


Hours 


Under 
weigh. 


Under 
steam. 


h 


841 
2211 
805 


2781 
2677 
1686 
1822 
2359 
2269 


6106 
3244 
4320 
6870 

218 
63808 
5795 
5393 
5370 
2668 

890 
1174 
5512 
5454 
1223 
6129 
5104 
63874 


284945 
5815 


2793 
1967 
1911 
3108 
2537 
3514 
1862 
2018 
525 2 
2107 
1671 
1485 
2168 
2320 
1969 
2285 
1924 
1017 
1424 
2162 


2543 
2528 20 


1904 


116152 30| 92733 


2370 1893 


m m 
25| 1462 15 
2077 50 
2556 15) 
2622 15 
2786 10 


30 
40 
1400 40 
25 
25 
55 
45 
50 
36 


2125 55) 


Results of Performances of the Steam-ships in 


Mean pressure of steam. 


Mean cut-off. 


ee ee 


Mean vacuum in condenser. 


0°65 | 0:50 


ots 


nae 


Notz.—Metre = 3:2809 feet = 393702 inches 


} 


<3 


1,935,570 
2,180,496 

543,000 
2,268,404 
1,704,550 
1,414,570 


1,259,626 
1,350,790 


3-46) 0°33} 2,081,867 | 1099 
0, = 220549 Ibs, Avoirdupois, 


Consumption of coal. 


| 2 

= a3 = ? 3 Pet 3 u 
¢| 8 Total g | Fe '|eul es 
Ble e | £8 leelas 
A Sie ewes lee 
= [2 |ERg* 
K kilo. kilo. | kilo.| kilo 
- 1483 465 | 40) 48 
2 1390 432 | 3-7| 46 
: 1533 450 | 41) 48 
; 1248 384 | 3:4] 3-4 
Fi 14380 411 | 3:8} 3-9 
52 1675 416 | 45) 44 
3 1586 462 | 4:9) 5-4 
: 1529 414 | 47} 5-0 

. 1605 489 | 45 

“6% 1547 477 | 51 

> 1644 495 | 5-4 

“62 1130 345 | 4:7 

Y 1222 369 | 50 

2 1268 423 | 53 

E 1215 336 | 5:0 

a 3,336,095 | 1191 387 | 4:9 

: 1,983,785 | 1008 318 | 4:2 

1:33} 1,906,803 997 800 | 41 

q 2,950,203 949 3809 | 4:7 

9} 2,470,000 | 972 315 | 48 

bd} 3,692,912 | 1051 348 | 5:2 

47 


372 | 49 
348 | 46 
366 | 59 
372 | 46 


St SUB HS G2 DH HH HS CHS OUT HS HS OT OT UH CUT Ou 
HK ROMTROTATWHHAAAR WK MARSHESAS 


348 | 4:3 
339 | 5-4 
354 | 5:6 
806 | 4-2 
300 | 4-2 
309 | 5-4 
303 | 5:3 


288 | 48) 5-0 
306 | 5:4) 53 
836 | 53) 57 
821 | 51] 5-1 
279 | S51} 55 
267 | 54) 5:2 
279 | 5-7) 59 
246 | +7) 48 
303 | 43] 53 
383 | 47) 5-9 
270 | 49} 59 
212 | 5:0} 5:7 
282 | 3:9} 49 
330 | 5:3} 55 
261 | 47} 55 

5:2] 5:2 


358 | 48) 5:1 


ON STEAM-SHIP PERFORMANCE. 


201 


the Service of the “ Messageries Impériales” of France during the year 1858. 


Consumption of 


oil and tallow. 3 
B= | 
s 
pele 
n 
° 5 Zz 
Fe a) oO 
Total. 3 Py 
uo 
= a s 
i] 
o oO 
5 & S 
Ay 
kilo kilo knots 


. (184943 |10°521 


3774 | 0-214) 9:21 


Mean speed estimated. 


8:81 


9°30 


9°82 


peed 
of nine knots, 


Consumption of fuel per 


mi 


le reduced to the s 


oo He Be 
ict 


78 
352 


iS) 


Go 09 
— 
02 GO 


303 
329 


bo 
=I 
or 


291 


SSSs 
2 8 6 
© He O> 


Co poe 
Nol &) 
= 


35 

287 
246 
296 


300 
348 
458 
402 
359 
381 
450 
429 
298 
311 
308 
332 
275 
269 
282 
275 
277 
354 
297 
224 
232 
224 
499 
586 
293 
401 
359 
445 
287 
211 


16782 
342 


Distance run with 1000 
kilogrammes of coal at the 
speed of nine knots. 


métres, 
13,517 
14,684 
15,766 
16,939 
17,729 
18,311 
16,878 
20,181 
14,181 
13,741 
14,025 
18,843 
18,299 
13,096 
14,096 
15,592 
19,341 
22,547 
18,713 
18,472 
15,962 
12,673 
13,804 
15,484 
14,575 
12,338 
12,945 
18,639 
17,820 
15,494 
16,715 
20,165 
20,595 
19,668 
20,160 
14,723 
15,667 
18,652 
24,802 
23,856 
24,781 
11,120 

9,469 
18,985 
13,851 
15,460 
12,465 
19,318 
26,208 


| 


31,295 
16,945 


202 REPORT—1860. 


Appenpix IT.—Taste 1. Chester and Holyhead Railway—Steam-boat 
Express and Cargo Boats, under regulated conditions of Time, 


Passages. 


No. Average Agius 

of rate of jweight 
Vessel. Date. trips ed | “pn 

run, miles. |valves. 


5 1859. hm h h lbs 
Eupress: 1 Jan. to 31 March ...| 73 | 8 24%) 4 0 | 449 | 13-40 | 1 
reek 1 April to 30 June ...| 47] 7 380] 420 | 4 37 | 1364 | 15 
eg ta hota & 1 July to 30 Sept. ...} nil. 
1 Oct. to 31 Dee. ...... 36| 526| 424 | 449 | 13:08 | 15 
1 Jan. to 381 March ...} nil. 
Carebtia 1 April to 30 June ...| 836 | 5 29] 417 | 431 | 18:95 | 15 
a sr 1 July to 30 Sept. ...|75| 516] 413 | 427 | 1415 | 15 
1 Oct. to 31 Dec....... 44| 555| 421 | 441 | 1845 | 16 
1 Jan. to 31 March ...| 81 | 7 28%} 4 6 | 445 | 1326 | 15 
ate 1 April to 30 June ...| 34] 6 48] 416 | 440 | 1350 | 15 
ware ards 1 July to 30 Sept. ...| nil. 
1 Oct. to 31 Dec....... 41| 615] 420 | 449 | 1308 | 15 
1 Jan. to 31 March ...| nil. 
1 April to 30 June ...| 37] 5 0} 4 7 | 430 | 1403 | 10 
Telegraph ...... 1 July to 30 Sept. .../83| 6 7] 411 | 4 40 | 1350 | 10 
1 Oct. to 31 Dee. ...... 40| 6 O| 427 | 458 | 1268 | 10 
Sarge: 1 Jan. to 31 March ...| 77| 917 | 5 40 | 6 44 | 1039 | 15 
hee 1 April to 30 June ...| 76 | 9 27] 5 44 | 6 28 | 1083 | 15 
oir ae a 1 July to 30 Sept. ...| 63 | 8 33] 545 | 635 | 1063 | 15 
1 Oct. to 81 Dec....... 77|1215| 540 | 6 47 | 10:31 | 15 
1 Jan. to 81 March ...| 26} 1115] 615 | 755 | 884 | 12 
1 April to 30 June ...| 87 | 9 25 | 555 | 6 22 | 10-41 | 12 
sors 1 July to 30 Sept. ..... 75 | 12 45| 6 0 | 727 | 939 | 12 
1 Oct. to 31 Dec. ...... 49|1335| 635 | 816] 846 | 12 
1 Jan. to 31 March ...| 71]10 O0| 715 |] 8 3 848 } 10 
1 April to 30 June ..| 7{| 8 5| 7 O | 728 | 9:37 | 10 
bess! 1 July to 30 Sept. .../ 28/1115 | 6 O | 6 57 | 1007 | 10 
1 Oct. to 31 Dec....... $9). 11-15'-615 | 738 (1937) 18 
1 Jan. to 31 March ...| 56113 5| 545 | 656 | 1009 | 12 
1 April to 30 June ...| 65 | 735| 530 | 6 14 | 11-23 | 12 
1 July to 30 Sept. ...| 75 | 730| 520 | 6 7 | 11-44 | 12 
1 Oct. to 31 Dee. ...... 91 | .8 20} 5 20 | 6 30 | 10-76 | 12 


ON STEAM-SHIP PERFORMANCE, 203 


Department.—A Return of the Speed and Consumption of Coal of the 
Pressure, and Expansion, for the undermentioned Period. 


Coals consumed. 


Average 


Proportion of Per trip Per hour Per hour 
pressure] steam in cylinder. | including | including | exclusive of Remarks. 
aE getting up raising raising 
steam and | steam, bank- | steam, bank- 
while lying ing fires, ing fires, 
at Holyhead. &e, &e, 
Ibs. tons cwt. Ibs. |tons cwt. lbs. |tons ewt, Ibs. 
ir) iS a 121112 | 213 47) 2 30| * Heavy gale, W.N.W. 


bo b 


13 | f¢and none | 111714 | 211 40| 119 28| — Based engines. 


123 | 18andnone | 1210 3 | 211 101} 119 79 
133 26 11-15 37 | 212 11] 119 80 
133 2s 12 211 | 214 33} 2 1 50 
133 ze 138 17 66 | 219 28) 2 6 45 
12 coe 13 138 59 | 217 65) 2 5 63) * Heavy gale, W.N.W. 
19,|} “fzond2e | 12 998 | 215100; 2 3 98| Based engines, 
103 18 1813 71 | 216 90} 2 4 71 
HEPER  fecetezs000...-: 12 17 60 | 217 15) 2 4 35 
10 none Ther e | an A O82 oe lO 
93 none 1418 25 | 219 41) 2 6 65 
7s of) ISelswU 2S SS |p els ais 
7 a 13 13 54 | 2 2 32|/ 114 12 
7s 38 1415 96 | 2 4101} 116 78 
7s a8 1413823 | 2 4 23) 116 O 
103 none Sell64 | 11s 7 17 98 
RENN fr cers << :-+-5s-- 8) 895621) ll 618) 4k 
11 none GolD 28 \eil eT rAO 17 39 
103 none Cha) ZU de ale ste) 17 88 
9 none Qre2r dey ale 2ae72 isi alg 
TUM Niece so. .00e. 102 6£.| tit) 16) V. 6 i 
8 none 9: Te24-| 1 8+ 36) 1 3983 
| 83 none 11 221 |} 1 9 48] 1 4 95] Norg.—Orders are given 
to the vessels, in gales and 
10 | 2nd grade ll 724/112 86] 1 4 45/heavy head sea, to ease 
10 | land2 grade | 10 861 | 113 51} 1 5 10) the engines, which occa- 
10 | land2 grade | 10 11 20 | 114 54} 1 5 _ 6/sionally increases the ave- 
93 | land2 grade | 11 1812 | 115 39) 1 6 103) rage passage. 


and full speed 


204 REPORT—1860. 

Appenpix IJ].—Tarie 2. Chester and Holyhead Railway—Steam-boat 
Department.—Chester and Holybead Steam-boats’ Consumption of Coal 
for the Six Months ending 30th June, 1859. 


Total as shown 
b 


Num- Average mm, y 
Th th Total f 

Name of vessel. pees . = i pe i oe oe the sitar pair rasta 

coal on board. 

1859. tons ewt. Ibs. tons cwt. lbs. tons cwt. Ib. 

Anglia. ies cose roma oF li iy df] 147315 78] 1458 8 0 
Cambri March 31. 

sao a June 30 ... 11 15 37 493 11100| 426 4 0 

Bookin 2a. ho. pone 1313 591) 1532 11 47] 1575 13 0 
March 31. 

Telegraph ....... June 30 ... 12 17 60 476 8 92| 49812 0 

Hibernia ......... pores 13 13 b4f| 210918 23] 2104 19 0 

Hercules «........ Earring Sil Gfl) 533 18 94.) 585 15. 0 

Ocean seve son a nie? Wi eoraie “0 | p28 Th 

Sea Nymph...... Pet. ce Mgowar tls eae ee 

8137 0 31] 8202 3 0 


AprenpDIx II.—Tasre 3. Chester and Holyhead Railway—Steam-boat 
Department.—Chester and Holyhead Steam- boats’ Consumption of 
Coal for the Six Months ending 3lst December, 1859. 


1859 tons ewt, lbs. tons cwt. Ibs. tons ewt, Ib. 
Anglia ...sses.- {res | 36 | 1210 3 | 450 0108| 44917 0 
Cambria ......... Pept 30 | Te aay eat |) Wsle1l eeyaaieg 1000 
Sle RO {esr | 41 | 131371 | 56018111] 568 6 0 
Telegraph ......\{ Dees | fo | 1413 25¢| 170811 60] 1688 3 0 
Hibernia ......... {RPr sy? | 8 | i213 a3 f| 206015 91) 2074 16 
Hercules .......-. SPE EO ee ty 1087 12> be | ames aes 
Dcomtee ee {ree re dE 
Sea Nymph...... ort a ie ta ie + |; 1852 1b 1d iaeeeceee 

9820 14 27] 9823 


205 


ON STEAM-SHIP PERFORMANCE, 


*‘sUTeTOY 


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———— 


soouisug ys —SSCSCSCSCSSSSOSOOOOSOCOCOSSCOSSSSO:~C~CS TATU QUITTING, 
Noms -- aa a a PCLIAGING) 
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"——— "on adviog § JaWUILIIG *Z TIGV[.— ]]] XIGNaday 


206 


2 


ON STEAM-SHIP PERFORMANCE. 207 


Aprrnpvix JII—Tasrez 3. Peninsular and Oriental Company's Engineer’s 


Log. 
| 
aoe: 2 
4 o 2 2m 3 
i) 1 eH u = H Cay Se fe) 
q m ns a a 3 sv rc) o.|9 
3! 2 a] a a see I are es ‘dd _Joslofl/e. n 
dial & | 23] 8 |E5] & |3s/84)/ 88/238] a8] = 
B/Si/o; ® ee S| SB Sa |Gopeang let | as (0) = 
Date. o|e v 3B 10'S as} °o © | ssh hy bservations. 
O} ey a 2 S) 2S a = ee ad (eo Us = | 
Hels] 6 | os] ss] © l|eS| oe] 89] BE) BS] 3 
Bao Af SiS (ier | Se are |) Smee acy el eae 
o| 3 ya | = 8 & z O°} 90] & 
a) eB |g Bere patie oie 
o Ea iS) 
AppENDIx II].—Taste 4. 
Yard. 
Report of trial of Her Majesty’s steam vessel 
Date 
TIRE TIRES coc etic ccs sa ccece cece catesecececsavastevevedess 
REED Mee, Sync detache cakes eIdeehecd sa havadeasd divas 


Draught of water... { “Aft 


_ Number of revolutions of the engines ...............6.:00000 


BreRSHeR OU Mateby VALVE. .......c6ssccsccsesececeesseccacessensons 
MURR TE CONCENSCES « oi.cc5sascdedet odetaceLobadscencoetcdecass 


merower-as shown by indicator .............cccsssccsccseneseteeees 


o 


SRMES DEE C res tate apd svdcdocs tee. fa cbs deehewsesecasetuedaneds 


Indicator cards and tracings are attached to this Report. 


Remarks as to the performance of the engines, boilers, &c. 


Revolutions of aie 7 
No. of runs. exigines per minute. time. pore Mean speeds. peed 
Min. | Sec. 


| | EE 


Knots mean 
| of means. 


[Note—Appendix III. No. 5 carried to bottom of Tables opposite page 216. 


- 


208 REPORT—1860. 


ApprenDIx IV.—Tasce showing the Ratios between the indicated Horse- 


indicated Horse-power ; 


Name of vessel. 


VESSELS OF THE Unitep States Navy. 


Niagara (screw) Performance in smooth water 


Place and nature of performance. 


Ordinary actual performance at sea under 


also, between the grate and heating sur- 


Statute miles. 


$i. | Voasinenniesnabuas esas <ch’s cdadbaasnwe neve’ 
steam alone.s.sc.<cscs-cccespaees eee eee 
Sic \ weadacemerpenne ens haces ieiadeshoweveceen Ditto ditto, steam and square sail combined|11°51 
Ay. A avasgestpasenes seadatensersesdaesbadenseds Ditto ditto, steam and fore-and-aft sails...| 8°55 
ry) apbboseacastagcdo pce conenerecn et Conds Mean of the above sea performance......... 9°75 
Massachusetts (Screw) ....ssseceecsersereesees Performance in smooth water ............00+ 
ary i, WRI Gabor cnoatco. cote boscodoceantiqanc Ordinary performance at sea under steam 
BIONE ...,.0%.se0cceekeasists's deus sepanctnceoeee tet 
Sey Neha ciueaectat entre tears ieene asec Ditto ditto, steam and sail combined ...... 
Be CORR ees Necacemmconeamnedsas sent Mean of the above sea performances ...... 
VessEts or THE Roysn Navy. 
attler (screw ))i.ss-cccsossteccese<teonsvenosu0 On trial, Thames, Sept. 5, 1844 ............ 
ST lo rets tenia scae caece cat van chimtenatlenwes Ditto ditto Jan. 1845 ctasseecnaceen 
Fy) be casduenececcietedea teres d-cussauacecedensd Ditto ditto  Sept..5, 1851 .o.....0.0.2 
Sate WE cnet OM rcahnaek Glan de tenceetakeousasedes Ditto ditto Sept. 5, USS] « Stegivessask 
PiNdeMN(SCLEW)|.sece0— cavsmastesaseeaseeeesa4 .|Ditto, Stokes Bay, Oct. 20, 1857 ............ 
sh RAPIER EOE Corer Tee Mercreconcne ey ‘|Ditto ditto Oct. D1 ie hee 
Reh ME MsiewCecscssaesageteceteuncuesevepeeess as eae (Ditto ditto Nov 757.45 ee 
ay VL besiae canhapacscerages cece nants tentberst Ditto ditto Dee? 1, ae 
Phe Heaton eet coccr er scl Oaeae Ditto ditto Jansd 1858. ose 
gy was thversh Scents oss wetese neotauee ease eS Ditto ditto April 16, 1858 
WOVIS (CREW)... scrsnocsvecderspate ce tesecteer se Ditto, Stokes Bay, May 27, 1859............ 
3» (with common screw)...........+2+00++ Ditto ditto April : 21, 49, ecnuranaceel 
y, (common ser#w increased to 20) ...|Ditto ditto May 5,— 3, ieescnerete 
» (Ditto, with two foremost corners 
CUE NSED)) Paes oa de eee ep eee ede set Ditto ditto May 9, %,,. Weeseteue 
», (Ditto, with four corners cut off) .../Ditto ditto May 23, 5;  sectesstacee 
yy (TEENS RCKEW)!.;... accesses anesedee Ditto ditto May 25, 5, saeeetee 
» (Ditto ditto) ..|Ditto ditto May 27, 4, ss.sseerees 14 130 12-266} 
» (Ditto ditto) Ditto ditto dune $3, 5, sitvscateae 14:006 |12°15 
Marlborough (screw) ...sccsccecceeseeneeeees Ditto, Stokes Bay, June 1, 1859 ............ 12-94 
Bi es Soest ee ae Ditto ditto June 2, 4, sserseeveeee 12-92 
_ (with half-boiler power) ...|Ditto ditto DUNE D, 59 cevbecnanare 10-62 
A Ds 2 ae ee a ee Ditto ditto May 28, <5; <cbvecsweeee 12-24 
Mersey (Screw) <cte.0s<soecessacscosevevavouses Ditto, Stokes Bay, March 23, 1859 ......... 15-31 
(Renown: (screw) Sccseveecaceetvotneatwercas ies Ditto, Stokes Bay, April 19, 1858 ......... 12-902 |11-2 © 
Pe Pree SAM nS test ishicerd: notice Ditto, between Sheerness and Nore, Oc- 
LODER Og Ope ssacees «+. cosets suze saaceaneorsee 12-533 {10-88 
$50. | levesaswaies tc kocia ee gate eee OR ERT CEE Reon Ditto, between Sheerness and Sunk Light, 5 
October S07 feac.s.ccer.ceceoscne saeealeee 12-533 |10-838 
j5: .. cemvarapiebean semnebercevoubpans emt netors Ditto, between Sheerness and Swim Middle, | 
October, SO: TBAT. wins sisecgacacsnnceneumens 14-573 |12-65 
Oy. hesdaccutegabanecereeccesescenetmeetmenee es Ditto, down the Swim, October 30, 1837 .. 


-|14:573 [12°65 — 


oven 


ON STEAM-SHIP PERFORMANCE. 209 


power and the Grate, the Tube, the other heating and total heating surfaces and the 
faces, and between the indicated Horse-power.and the Coal consumed. 


. ic} fe} o * 5 
>) . Pr ene ap o obo fet tH 
Horse-power. og ee [es] 38 | ac oo S as | os Sy g. 
= -— Ps oF CE 62 "39 EPPS BSeé aa cs] as 
=0 se BO Rie) eee (ea as @H be ge. 3o.D 
sa 22 |Hal Ba aon | $3 2a ne 2° esh on 
—<———— a. Sem 57 st ago and On a2 [me] ae) oH 
32 So ag a? CE we oe HO mod Sd e go 
: Be | ge |os| $2 | 888 |a88| S2 | $8 |) BES) SBS] Se 
Be d Ba | £3 |sa| 4 (S25 /8e3'| $3 | S21 888] Fee] Fe 
3 g So | Sg | ho! =o leek loot] H8 | oS | sea] Saez] Ss 
S] d ox S [es] SB ogo] °30| Sm 29 a= HHS ot 
g 5 23 2.8 | os a cosa | ofa = °° on asa @¥ 
EI eq jase ios | 29 |S 28 gS | 88/48 eS aO 
4 A es a8 BS) $3 ae a ‘S @n 3 2) cd Sa 
a A | a4) al | & i é ma | § = 
: | Ibs. | Ibs. | Ibs. 
1955-09 | 700 858 | 2-793 | -247| 6-556) 2-192) 8:748 85°386| 334) 3-529 


879-28 | 700 796 | 1-256 | 55414577 | 4873 19-451 |35°336| 334) 4-617 |41-813| 9.058 
77365 | 700 “905 | 1-105 | -625 16-567 | 5-538 22-107 \35°336| -334) 4-904 42-743 8-716 
837-31 | 700 *836 | 1:196 | -57815°308 | 5°117 |20-426 |35°336| 334) 4-987 |42-156) 8-452 
824-48 | 700 849 | 1:178 | -587\15-546 | 5-197 |20-744 |35°336 |- -334| 4-790 |42-269| 8-597 


(240-74 50° oe axe toll 


% (|10-280 10-281 |28:448) ... | 4-029 

—-168°81 30: oat w. =| 514 ie 14-661 |14:661 |28-448} ... | 4-401 

149-61 ae ioe ... |°988) | & | |16:543 |16:543 |28-448|) ... | 4-491 

16254 set bars .» | 585) ) & \115:227 115-227 28-448} .., | 4-429 
428 200 467 | 2-140 


436°7 200 “458 | 2-184 
499-2 200 “401 | 2-496 
519-2 200 385 | 2596 


2324-42 | 800 344 | 2-906 | -234) 5-131) +991} 6-122 26-16 193 
2325:96 | 800 *343 | 2°907 | 234) 5°035| +987) 6-022 |26:16 193 
2663-60 | 800 300 | 3°330 |-204) 4:478| +865 | 5°343 |26-16 193 
2587-50 | 800 *309 | 3°234 |-210) 4609) +894) 5:503 |26-16 193 
2685:04 | 800 “298 | 3°356 | -203) 4441} -858)| 5-299 |26:16 193 
2979 800 268 | 3°724 |-183| 4:004| +773) 4:777 |26-16 193 


3091 800 "259 |3°864 |-176| x we | 4659 [26-47 
2921-2 800 278 | 3-652 |-186| ... we. | 4:929 |26°47 
(2788-4 800 287 | 3486 |-195) ... ... | 5°164 |26°47 


2884-4 800 | -278 |3-606 |-189| ... ... | 4:992 |26-47 
2920-32 | 800 | -274 |3-650 |-186| ... we | 4:931 126-47 
2825-6 800 *283 |3-532 |-192| ... ... | 5-096 |26-47 
3091-1 800 | -259 |3-864 |-176) ... ... | 4658 |26-47 
3009'03 | 800 | -266 |3-761 |-188| ... ... | 4:786 |26-47 


3022 800 265 |3°778 | :180| 3:947| -762)| 4:709 |26:16 193 | 
3054-26 | 800 *262 | 3°818 |-178) 3-905] +754) 4-659 26-16 193 
1722-08 | S00 ‘A465 | 2-153 | 316) 6°926| 1-338} 8-264 |26-16 193 
273894 | 800 292 | 3-424 |-199| 4-355 | +841 | 5-196 26-16 193 


4044 1000 247 | 4-044 | -168) 3:702| +736! 4-438 |26-40 198 


3183 800 | -251|3:9
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